Global air-sea flux of carbon dioxide (CO2) is calculated from wind data acquired by the satellite scatterometer QuikSCAT, the passive microwave radiometer AMSR-E, and the model reanalysis ERA-40 using four of the most commonly used wind speed dependent parameterizations of gas transfer velocity. Assuming QuikSCAT as reference, the results are compared to obtain an estimate of that relative uncertainty in the flux calculations which results solely from the origin of the input wind data. We illustrate the discrepancies between these data sets and quantify the uncertainty in the computed air-sea CO2 flux that arises from data processing such as temporal and spatial averaging using AMSR-E as an example data set. The impact of temporal variability of wind speed is shown to be significantly greater than that of spatial variability. However, simple parameterizations of temporal variability are found to be sensor-specific and cannot be applied in a straightforward way to data sets with lower temporal resolutions from other sensors. We show a simple methodology to correct monthly mean data in such a way that seasonally and zonally varying parameterizations of temporal variability derived from QuikSCAT data can be applied to data from AMSR-E and ERA-40. This allows us to produce a global 44-year time series of gas transfer velocity and to present a more coherent estimate of air-sea transfer of carbon dioxide from the three most commonly available types of wind data.
 Steadily increasing levels of carbon dioxide (CO2) in the Earth's atmosphere are of growing concern due to their potential impact on climate change and extreme weather events. While atmospheric concentration of the gas can be measured with relative ease, monitoring marine and terrestrial budgets is significantly more complicated. Estimates of oceanic uptake of CO2 from the atmosphere found in the literature vary between −1.4 Gt C/a [Wanninkhof and McGillis, 1999] to −3.7 Gt C/a [Takahashi et al., 2002]. While these discrepancies are largely due to the use of different parameterizations of the gas transfer velocity, k, the choice of wind data on which these calculations are based plays an important role since global estimates of wind speed show significant variability between products in the magnitude of spatial variability and regional and global means [Sweeney et al., 2007]. However, the selection of a wind speed data set is often influenced by practical issues such as temporal coverage and its quantitative impact on gas flux studies has not been adequately determined for state-of-the-art wind speed data.
 Air-sea flux of CO2 is described by
where k is the gas transfer velocity, s the solubility of the gas in seawater, and ΔpCO2 the difference in partial pressure of CO2 on either side of the air-sea interface. The solubility is a known function of sea surface temperature and salinity [Weiss, 1974; Wanninkhof, 1992]. Climatological values of ΔpCO2 have been produced by Takahashi et al.  based on approximately 940,000 measurements of pCO2 in surface waters excluding any observations in the equatorial Pacific between 10°N and 10°S during El Niño events [Takahashi et al., 1993, 2002]. The parameterization of gas transfer velocity remains an unresolved problem and while several parameterizations of k exist [Liss and Merlivat, 1986; Wanninkhof, 1992; Wanninkhof and McGillis, 1999; Nightingale et al., 2000], they all vary strongly in their predictions of k particularly for higher wind speeds as illustrated in Figure 1.
 There is a growing consensus that wind speed is unlikely to explain all of the variability observed in gas transfer velocities and some newer parameterizations of k include parameters of the wavefield [Glover et al., 2002; Woolf, 2005; Fangohr and Woolf, 2007]. Nonetheless, while these new approaches await validation, a common feature of the most frequently used traditional parameterizations of k is their nonlinear dependence on u10, the wind speed at 10 m height in neutral stratification. This makes wind speed the parameter with the strongest influence on the variability of our current predictions of air-sea CO2 flux. All other parameters are either well known, fixed or have a lesser impact due to a more linear influence on the flux. Given this fact, particular attention needs to be paid to the choice and quality of wind data used in CO2 flux studies as small biases of wind data can propagate to produce a much larger bias of the flux results.
 The advent of remotely sensed wind speeds has made global calculations of the gas transfer velocity possible [Etcheto and Merlivat, 1988]. Many studies of satellite-derived winds have been aimed at validating individual data sets against in situ or model data [e.g., Halpern et al., 1994; Boutin et al., 1996; Meissner et al., 2001; Mears et al., 2001; Ebuchi et al., 2002] or have compared data from different sensors [e.g., Boutin and Etcheto, 1990, 1996; Bentamy et al., 1999; Boutin et al., 1999; Queffeulou et al., 1999; Chen, 2003]. Boutin et al.  explicitly study the impact of data biases as well as gridding schemes of satellite wind data on calculations of the gas transfer velocity. They reach the conclusion that data from the NSCAT scatterometer are best suited for calculations of gas transfer velocity when compared with Special Sensor Microwave/Imager (SSM/I) and European Centre for Medium Range Weather Forecasts (ECMWF) winds. Because of the short (10 month) life span of NSCAT they recommend a continuation of their analysis based on QuikSCAT wind speeds. Carr et al.  compare CO2 exchange coefficients from the newer scatterometer aboard QuikSCAT with those from SSM/I for the year 2000 and find a discrepancy of 10% in the fluxes calculated from the two data sources.
 The objectives of this paper are to evaluate recent wind products, their relative accuracy and spatiotemporal variability with respect to calculations of air-sea CO2 flux; to develop a simple, seasonally and zonally varying parameterization of submonthly variability of wind speed and, based on this parameterization, to establish a long-term (44 year) record of global mean gas transfer velocity and air-sea CO2 flux.
 We study characteristics of the QuikSCAT scatterometer which has been in orbit since summer 1999, providing a continuous data record of >5 years to date. Using QuikSCAT winds as a baseline, we compare its data to wind data from the AMSR-E passive microwave sensor and the model reanalysis ERA-40 by ECMWF. It is not in the scope of this paper to provide a general validation of these data sets since no in situ data are used. The data sources are compared in their most commonly used form (i.e., gridded to a standard geographical grid) when applied to calculations of the net air-sea CO2 flux with a view to identifying the differences that arise from their relative biases and spatiotemporal characteristics.
Section 2 gives an overview of the different data sets we use in this study, highlighting spatiotemporal resolution and other data characteristics relevant to gas flux studies. Section 3 combines data analysis and results of our investigation; we first present some quantitative estimates of global gas flux based on these data sets and analyze the variability of the results in part 3.1. In section 3.2 we address uncertainties arising from spatiotemporal averaging of data and then we propose a method of parameterizing temporal variability of the data in a sensor-independent way in section 3.3. This methodology is applied to 44 years of model reanalysis data to obtain a long-term time series of global transfer velocities and gas flux, based on the most recent estimates of variability of wind speed and sea surface temperature over this period. We discuss our results in section 4 and summarize our main findings in section 5.
 The monitoring of global winds as an input to ocean models and for other applications has received a lot of scientific attention over the last decades, resulting in a wealth of publicly available data sets. The diversity of sources has led to good cross-validation of many of the available products [e.g., Boutin et al., 1999; Wentz et al., 2001; Chen, 2003; Caires et al., 2004]. However, subtle biases between data products are often overlooked or assumed negligible, but can play a significant role in the context of gas flux studies due to a nonlinear dependence of the gas transfer velocity on wind speed. Furthermore, spatial and temporal averaging and interpolation schemes used to prepare gridded data sets are not always well documented, but become important when the products are applied on a global scale. The temporal and spatial sampling characteristics of all data sets used in this study are summarized in Table 1 and will be explained in the rest of this section.
Table 1. Overview of Temporal and Spatial Characteristics of the Data Sets Used in This Study
1° × 1°
12 h/1 month
1° × 1°
12 h/1 month
0.25° × 0.25° – 1° × 1°
1.5° × 1.5°
Reynolds OI SST
1° × 1°
1° × 1°
Takahashi et al. ΔpCO2
4° × 5°
2.1. Scatterometer Data
 Scatterometers are the most common remote sensing instruments used for the global monitoring of wind speed and direction. While their spatial resolution is limited and on the order of several tens of kilometers, daily coverage is achieved in most global regions except at the equator and mature algorithms exist for data analysis. In this paper we mainly focus on data from the scatterometer on board QuikSCAT, although some data from the European Remote Sensing satellites (ERS) were used for comparison.
2.1.1. QuikSCAT Data
 The SeaWinds scatterometer on QuikSCAT was launched in June 1999. It operates at 13.4 GHz (Ku-band) with a swath of 1800 km. Daily coverage is about 92% of the global ice-free oceans. Measurements of wind speed and direction have a typical RMS difference of 1 m/s and 20° when compared to buoy data, its highest spatial resolution is 25 km [Ebuchi et al., 2002], gridded onto a 1° × 1° geographical grid. We use data processed by Remote Sensing Systems (RSS) as version 3, using their Ku-2001 algorithm [Wentz et al., 2001]. Compared to previous versions which exhibited an overestimation at high wind speeds [Ebuchi et al., 2002] Ku-2001 has a flatter radar backscatter versus wind speed response at high winds. The measurements obtained by the sensor represent a time average over approximately 8–10 min.
2.1.2. ERS Data
 The advanced microwave instruments (AMI) aboard the ERS satellites were operational between 1991 and 2003. Data were acquired at C-band (5.3 GHz) and a swath width of 500 km, with an accuracy of 2 m/s or 10% in the range of 4–24 m/s and a directional accuracy of ±20°. The ground resolution of the scatterometers is 50 km × 50 km. The wind vectors are computed with the CMOD-IFR2 model developed by the Department of Oceanography from Space at IFREMER, which brings significant improvement over the ESA near-real time product distributed to the European meteorological centers [Quilfen and Bentamy, 1994; Boutin and Etcheto, 1996]. In order to construct averaged synoptic fields from discrete observations over each time period, a statistical interpolation is performed using an objective method (kriging) onto a 1° × 1° geographical grid.
2.2. Passive Microwave Data
 The Advanced Microwave Scanning Radiometer (AMSR-E) is a passive microwave instrument aboard NASA's Aqua satellite launched in 2002. It operates 12 channels at 6 frequencies and covers a swath of 1445 km. The AMSR-E ocean products used in this study were produced using a modified version of the ASMR-E Direct Broadcast algorithm developed for NASA, using an on-orbit calibration method developed at RSS to convert counts to brightness temperatures [Wentz et al., 2003]. We use RSS version 4 data which are gridded onto a global 0.25° × 0.25° grid. The target accuracy of AMSR-E for wind speed retrieval is 1.5 m/s in the range of 0–30 m/s [Earth Observation Research and Application Center, 2004]. Comparison of AMSR-E wind speed data to those acquired by the QuikSCAT scatterometer show a positive bias for AMSR-E of approximately 0.5 m/s [Wentz et al., 2003], although these comparisons are based on high latitude collocated data points only. The target accuracy for measurements of sea surface temperature (SST) is 0.5°K in the range of −2°C to 35°C [Earth Observation Research and Application Center, 2004].
 While the simultaneous acquisition of wind and sea surface temperature data appears attractive for the calculation of gas flux, problems with the instrument's model function in high winds produce a systematic loss of SST (and thus gas flux) data in these conditions, producing a significant negative bias in the calculated flux. This is no longer a problem when monthly mean SST values are used but this removes the advantage of coincident SST and wind measurements. As a result we use SST model data (see section 2.3.2) for consistency throughout the study.
2.3. Model Reanalysis Data
 Apart from satellite data which have become more easily available and reliable over the last decades, model reanalyses are another source of long-term global data sets for air-sea flux studies. Reanalysis data promise to be the future tool combining all data sources into one coherent system and are continuously being improved [Caires and Sterl, 2001]. Despite these efforts there remain some inhomogeneities which result from varying levels of data available for assimilation, particularly during times when data coverage was insufficient to constrain intrinsic model variability. This is illustrated, e.g., by Sterl  in a comparison of ERA-40 and NCEP/NCAR reanalysis data. Data variability likely to be caused by insufficient in situ data coverage to constrain the reanalysis models is largest over the Southern Ocean in the 1950s and 1960s and significantly reduces after 1979 with the onset of remote sensing. Sterl  highlights that pre-1980 long-term variability in the Southern hemisphere might reflect the increasing amount of data rather than true changes; in the Northern hemisphere these issues are much less severe.
 Previous studies comparing model reanalyses data products have recommended the use of the ERA-40 data set for global wind and wave studies. This is based on good agreement with buoy data and statistically smaller errors than other reanalysis data sets such as, e.g., NCEP-NCAR [Caires et al., 2004]. Accordingly, ERA-40 data are used in this study.
2.3.1. ERA-40 Data
 The objectives of the ECMWF ERA-40 project are to produce and promote use of a comprehensive set of global analyses describing the state of the atmosphere, land, and ocean-wave conditions from mid 1957 to August 2002. The ERA-40 project applies a modern Variational Data Assimilation technique (used in daily operational numerical forecasting at ECMWF) to the past conventional and satellite observations, including wind speeds from SSM/I and ERS and significant wave height measured by satellite altimeters. Data sets are available at 6-h temporal resolution on a 1.5° × 1.5° geographical grid [Uppala, 2001; Kållberg et al., 2004]. This high temporal resolution does not always represent the true resolution of the underlying input data which, in some cases, can be linearly interpolated between data points spaced further apart in time (e.g., monthly averages) [Fiorino, 2004]. For the purpose of this study only monthly mean fields of ERA-40 wind data are used.
2.3.2. HadISST Data
 The Hadley Centre sea ice and sea surface temperature data set version 1 (HadISST1) provides continuous values of global sea surface temperature on a 1° × 1° longitude-latitude grid from 1871 to the present on a global scale. HadISST1 compares well with other model analysis data sets but contains SST fields with more uniform variance through time and more realistic month-to-month persistence than some of those previously published. The HadISST1 data set has been used to supply information for the ocean surface for the period 1958 to 1981 in the ERA-40 reanalysis [Rayner et al., 2003]. Figure 2 shows a comparison of monthly averaged HadISST SST data with SST from the Reynolds and Smith  optimal interpolation (OI) data set for the year 2000. The two data sets show excellent correlation (r2 = 0.997) and have an RMS difference of 0.61°C. For the purpose of this study we have used HadISST SST data, but due to the relatively small influence of temperature on gas flux (compared to wind speed) and the similarity of the data sets, our results are very similar when using Reynolds and Smith  OI SST.
3. Data Analysis and Results
3.1. Variability Between Wind Data Sets
 For the calculation of gas transfer velocities we use standard wind and temperature products as described in the previous section. All of the data are gridded to 1° × 1° and monthly averages are used while wind distributions on a submonthly scale are parameterized using 12-hourly QuikSCAT data. For calculations of the air-sea flux of CO2, climatological ΔpCO2 fields by Takahashi [Takahashi et al., 2002] for 1995 were used. Accordingly, interannual variability in our results only represents that variability due to variations in the wind and temperature data since the partial pressure difference across the air-sea interface is held constant between years. The [Takahashi et al., 2002] data were regridded from the original 5° × 4° to 1° × 1° spatial resolution to match wind and temperature data using cubic splines. For all calculations, monthly HadISST sea surface temperature data were used and salinity as supplied with the Takahashi et al.  data set, provided by the National Oceanographic Data Centre . Schmidt numbers were calculated according to Wanninkhof .
 The ΔpCO2 fields as provided by [Takahashi et al., 2002] are unlikely to adequately represent highly variable conditions in many shelf and coastal areas due to a lack of input data. If as proposed by Borges and Frankignoulle  many shelf seas are exceptionally strong sinks our climatology in common with others based on Takahashi et al.  may underestimate the oceanic uptake of CO2. Furthermore, we do not account for effects of diurnal warming of the surface layer or the cool skin of the ocean [Ward et al., 2004; McGillis and Wanninkhof, 2006; Zhang and Cai, 2007], two processes which have opposing effects on the overall gas flux. Calculations are based on wind speeds for neutral stratification of the marine-atmospheric boundary layer and any additional effects of stratification [e.g., Erickson, 1993] are excluded.
 We apply four of the most commonly used parameterizations of gas transfer velocity for short-term wind measurements published by Liss and Merlivat  (LM′86), Wanninkhof  (W′92), Wanninkhof and McGillis  (WG′99), and Nightingale et al.  (N′00). The specific equations used for the parameterization of k are given in Table 2. These parameterizations are applied to the various wind data sets to calculate annual global transfer velocity and net atmosphere-ocean Carbon flux; the results are summarized in Table 3. In all cases we use monthly wind data from the respective satellite sensors and account for submonthly variability of wind speeds by applying climatological correction factors derived from 5 years of 12-hourly QuikSCAT data on a 1° × 1° grid following Wanninkhof et al. . Since there is no temporal overlap of all three data sources we average over a number of years depending on the individual data record.
Table 2. Parameterizations of gas Transfer Velocity k Based on Wind Speed, u10, Used to Calculate Global Fluxes as Shown in Table 3 (Sc Stands for Schmidt Number)a
 As can be expected, there is substantial variability among the results obtained using different k parameterizations, reaching up to 300% between LM′86 and WG′99 for AMSR-E wind data. There is however also strong variability in the results obtained from different wind data sources, most notably when using the cubic relationship of gas transfer velocity and wind (WG′99). The differences between global flux results based on ERA-40 data and those based on scatterometer data from QuikSCAT are 25% for W′92 and 32% for WG′99, mean transfer velocities vary on the order of 20% between these parameterizations.
Figure 3 illustrates the cause of these discrepancies by studying the wind speed residuals between two monthly averaged data products as a function of average wind speed from both data sources, along with a histogram of annually measured monthly mean wind speeds (note the different scaling of y axes in Figures 3a and 3b). Figure 3a shows a comparison of wind data acquired by QuikSCAT during 2000 and data for the same year from ERA-40. There is a clear trend in the residuals showing that, on average, QuikSCAT wind speeds exceed ERA-40 values over the entire data range. This bias is small (<1 m/s) at average wind speeds up to 11 m/s. It increases with wind speed and exceeds 10 m/s above an average wind speed of 17 m/s. Figure 3b shows the same comparison for QuikSCAT and AMSR-E data for the year 2003 with similar results. At wind speeds below 6 m/s AMSR-E wind speeds are, on average, greater than those measured by QuikSCAT. Above 6 m/s QuikSCAT winds exceed AMSR-E wind speeds but the differences between the data sets are smaller than those observed between QuikSCAT and ERA-40. The discrepancies between the data sets increase with wind speed and reach up to 5 m/s at a maximum average wind speed of 20 m/s.
 Both of these findings suggest that either QuikSCAT provides better capabilities of capturing high wind speed events or it overestimates winds at high wind speeds. Earlier versions of QuikSCAT data have suffered from overestimates at high wind speeds but an improved version of the model function, Ku-2001, has been designed to reduce this effect in version 3 data (D. Smith, personal communication, 2005). The consistency between results from the two scatterometers (QuikSCAT and ERS AMI) and comparison of wind speed histograms of the various data sources (not shown) suggest that a negative bias of ERA-40 and AMSR-E at high wind speeds exists, resulting in a reduced net oceanic uptake of CO2 when wind data from these sources compared to QuikSCAT winds are used.
Figure 4 shows a similar comparison of these three data sets, now plotted against sea surface temperature. Dependence of differences in wind speed on SST is potentially important since it could distribute the effect of the errors preferentially to impact areas tending to ingassing or outgassing of CO2 according to the solubility control by SST. Figure 4a illustrates that wind speeds from QuikSCAT exceed those of ERA-40 in all regions but that differences are greatest in those areas exhibiting particularly high or low SST. The latter may be due to ice contamination of satellite wind speeds. Figure 4b shows a different scenario for QuikSCAT and AMSR-E, where AMSR-E wind speeds exceed those measured by QuikSCAT in areas with 24°C < SST < 32°C. There is a substantial number of pixels falling into this category, which are located in the tropics, often associated with an oceanic source of CO2 to the atmosphere.
 Thus in comparison to QuikSCAT, AMSR-E data may exaggerate the outflux in tropical regions, reducing further the calculated global net uptake of CO2. This is reflected in the results shown in Table 3.
3.2. Spatiotemporal Resolution
 The high variability between wind data from different sources raises further questions about the accuracy at which wind data are required for gas flux studies and whether that accuracy can be realistically obtained from remote sensing or model sources. Progressively higher resolution broadens the distribution of wind speed and results in higher transfer velocities from the nonlinear formulae. Wanninkhof et al.  show that calculations based on the assumption that wind speeds are Rayleigh distributed are unrealistic and introduce regionally and globally significant errors in air-sea gas transfer velocities and gas fluxes.
 On a spatial scale, data are provided at different resolutions ranging from the 5° × 4° of the [Takahashi et al., 2002] ΔpCO2 data to 0.25° × 0.25° at the highest resolution of gridded data from QuikSCAT and AMSR-E. The spatial resolution of different sources of wind data varies from 0.25° × 0.25° to 1.5° × 1.5°. It is unclear how strongly spatial resolution affects calculated gas fluxes under otherwise constant conditions.
 The findings of Wanninkhof et al.  indicate that high temporal resolution is important and at least requires parameterization in the form of correction factors to account for non-Rayleigh distribution of winds. If
This then allows us to rewrite equation (2) for monthly averaged wind speeds as
with R0 = R1 = 1. Carrying out these corrections at a resolution of 0.25° × 0.25° spatially and 12 h temporally requires a pixel-by-pixel calculation of Rn. This computationally intensive method is often abandoned in favor of using monthly mean wind speeds assuming a Rayleigh distribution in time [e.g., Zhang and Cai, 2007]. In order to reduce the error introduced by this methodology it is desirable to obtain simple yet more accurate correction factors to be used in studies of air-sea gas flux.
Table 4 quantifies the variability introduced into global flux results when the data are used at various spatial and temporal resolutions. We use the maximum spatial and temporal resolution of 0.25° × 0.25° and daily wind speed measurements as a reference point to illustrate deviations from this scenario in percentage of the high-resolution flux values. Monthly means are assumed to represent Rayleigh-distributed wind speeds, spatial averaging takes place over 320 (20 × 16) pixels to produce a 5° × 4° grid. All calculations are for data acquired during the year 2004.
Table 4. Net Global Carbon Flux for 2004 Calculated Using AMSR-E Wind Data at Various Spatial and Temporal Resolutions and the W′92 and WG′99 Parameterizations of Gas Transfer Velocitya
Deviations are given in % of the daily 0.25° × 0.25° results. For monthly values Rayleigh distribution of wind speeds with time is assumed.
 The results demonstrate the dominant influence of temporal averaging compared to spatial variability. The errors introduced by assuming Rayleigh-distributed winds lie between 6–9% for W′92 and between 29–30% for WG′99. These values slightly exceed the findings of Wanninkhof et al.  who quote 5% for W′92 and 26% for WG′99, based on NCEP winds. In contrast, errors introduced by spatial averaging do not exceed 3% for W′92 or 7% for WG′99, indicating that spatial variability of wind plays a less significant role than temporal averaging.
Figure 5 illustrates the seasonality of global air-sea CO2 fluxes for W′92 (Figure 5a) and WG′99 (Figure 5b) in 2004. The plots show monthly air-sea CO2 fluxes calculated from data at various spatiotemporal resolutions plotted against calendar month. The highest discrepancy lies between curves showing fluxes calculated from daily and monthly wind speeds during the boreal autumn and winter months. This trend can also be observed when comparing curves showing the effects of different spatial resolution, although the overall effect is nearly an order of magnitude smaller.
 The zonally averaged profiles of transfer velocity k shown in Figure 6 highlight the geographical location of these discrepancies for W′92 (Figure 6a) and WG′99 (Figure 6b). The plots show annual averages of k calculated from data at various spatiotemporal resolutions for the year 2004 plotted against latitude (y axes). Highest discrepancies are located predominantly at higher latitudes and are more pronounced between transfer velocities calculated for different temporal resolutions, while the impact of spatial resolution is nearly negligible.
 All of these results support the findings by Wanninkhof et al.  that studies of gas flux should be carried out using winds at the highest available temporal and spatial resolution or that the variability of wind speed needs to be parameterized appropriately. However, increasing spatiotemporal coverage increases computation time significantly and many data sets are not available at such high temporal or spatial resolution or do not represent submonthly variability of wind speed appropriately. This makes a parameterization of the relevant processes a potentially attractive solution. It would be particularly desirable to obtain a parameterization that can be applied to different types of wind data. The latter is complicated by the differences between data sets in monthly mean values and intramonthly variability which we discussed earlier.
 To illustrate this point further, Figure 7 shows the absolute values and differences between R2 values calculated (using W′92) from high resolution data acquired by QuikSCAT and AMSR-E, each sampling at 12-h intervals. Figure 7a shows the absolute values of R2 derived from 2 years of QuikSCAT data (2003–2004), while Figure 7b shows the percentage difference of R2 values calculated from AMSR-E data (2003–2004) from the numbers shown in Figure 7a. Comparison of R2 values derived from QuikSCAT and 6-hourly ERA-40 data produces similar results (not shown). Differences between Rn from the two sensors result from the generally higher intramonthly variability in the QuikSCAT data. Also, there are some deviations in regions suffering from low data rates due to frequent rain events such as the west Pacific and east Indian Ocean. Deviations for a cubic expression (WG′99) are generally larger. While average deviations between correction factors from the two sensors are relatively small with 5% for W′92 and 10% for WG′99, this masks the fact that in regions of high wind speed variability (e.g., in the North Atlantic) local values can be significantly higher. Overall we find that applying a set of correction factors derived from one sensor (AMSR-E) to the monthly mean data of another sensor (QuikSCAT) can result in air-sea CO2 flux values differing by 16% (W′92) or 25% (WG′99) for a given year on a global scale.
3.3. Generalized Correction of Wind Data
 We will now show a simple method to investigate the application of correction factors in a more generalized way and to a number of different wind data sets. To do this, we assume that out of the model reanalysis, passive microwave, and scatterometer data sets that we have studied so far, the scatterometer data present the most realistic measurement of wind speed, capturing the largest number of high-wind speed events which are important for calculations of air-sea gas flux and accurately representing both mean monthly wind speed and intramonthly variability. This is in general agreement with the findings of Boutin et al.  and as shown in Table 3 our results from the two different scatterometers (QuikSCAT and ERS AMI) show greater consistency than any of the other sensors. Accordingly, we base our method on the development of correction factors derived from high-resolution scatterometer data.
 Currently, the calculation of correction factors as described above is computationally expensive, especially when carried out at high spatial resolution, and is often abandoned in favor of using monthly mean wind speeds and assuming Rayleigh distribution in time [e.g., Zhang and Cai, 2007]. Since calculations of gas flux are relatively insensitive to spatial resolution our first step is to reduce this. Furthermore, most of the characteristic patterns observed in maps of correction factors follow zonal lines indicating that the main variability of the correction factors, Rn (see equation (3)), occurs along meridional axes. Accordingly we have used 5 years of QuikSCAT data to produce zonally averaged profiles of correction factors R2 and R3 at 1° resolution based on equation (3). These are then averaged into seasonal means to retain some temporal variability reflecting, e.g., storm track regions in the high latitudes during their respective winter months. These seasonal correction factors are shown in Figure 8 for the W′92 (R2, solid line) and WG′99 (R3, dashed line) parameterization. The values assuming a Rayleigh distribution of winds (R2 = 1.25, R3 = 2.17) are marked by two straight lines. The measured correction factors hardly reach this line for R2 and never for R3. This demonstrates why the long-term formulations of gas transfer velocity that assume a Rayleigh distribution of wind speeds lead to substantial overestimates of gas flux when applied to monthly mean wind data (as previously detailed by Wanninkhof et al. ). The plots show the zones of near-constant trade winds as zones of minimal variability (and accordingly low Rn factors) with values of R2 < 1.1 (R3 < 1.25) for December to March in the northern hemisphere and from April to November in the southern hemisphere. Both hemispheres show maximum variability at moderate to high latitudes with a peak at approximately 40° and another at approximately 60°.
 To assess the error introduced by the spatial and temporal averaging of correction factors, we tested our methodology using only 4 years of data (2000–2003) for the generation of zonally averaged Rn. These are then applied to an independent year of QuikSCAT data (2004) and the resulting fluxes compared to those calculated from the data at full spatial and temporal resolution. The difference in the net global flux is less than 0.6% which is a satisfactory result.
 However, before we can apply these simplified correction factors to data sets from different sensors, some modification of monthly mean values is necessary since we established earlier that these vary between different sensors or between remotely sensed and model data. Thus 2 years of coincident data from QuikSCAT and AMSR-E (2003, 2004) and QuikSCAT and ERA-40 (2000, 2001) are used for a linear least squares regression of zonally averaged monthly means. The regression is then applied to the remaining data set to produce QuikSCAT-like monthly means after which the zonally averaged correction factors derived from QuikSCAT data can be applied. The regression of 2 years of zonally averaged monthly mean wind speeds for QuikSCAT and ERA-40 and QuikSCAT and AMSR-E data, respectively, are shown in Figures 9a and 9b. The RMS errors of the two sets of data are 0.54 m/s (ERA-40/QuikSCAT, r2 = 0.90) and 0.28 m/s (AMSR/QuikSCAT, r2 = 0.97).
 While this methodology might appear somewhat simplistic it achieves reasonable agreement between transfer velocities computed for the various wind data sources as shown in Figure 10. The k values computed from 20 years of ERA-40 wind data (light gray, online green line) show some underestimations in the northern hemisphere during the winter months and an overestimation during summer. A potential source of discrepancy between the curves is the fact that we compare a long-term average computed from ERA-40 data with only 1 year of AMSR-E and QuikSCAT data. Furthermore, this particular year (2004) is not contained in the ERA-40 time period (due to a lack of overlap between the data sets) so some variability between the ERA-40 curve and the two others is to be expected. Since the largest discrepancies occur in the northern hemisphere during winter months, correlation with the North Atlantic Oscillation (NAO) index might explain some of the observed variability [Jones et al., 2003].
 However, deviations between the results from different wind sources are significantly reduced, thus delivering a largely unified result of global transfer velocities. On the basis of the corrections we have applied (linear regression of zonally averaged monthly means; R2 derived from QuikSCAT) and using W′92, globally averaged values of transfer velocity yield 21.3 cm/h as a 20-year average for ERA-40, 21.8 (21.3) cm/h for AMSR-E in 2003 (2004), and 21.1 (21.2) cm/h for QuikSCAT in 2003 (2004). On a regional basis, these results may need to be treated with some caution due to some systematic deviations such as low values exhibited by the ERA-40 curve over winter months in the North Atlantic. However, results on a global basis are encouraging.
 Furthermore, our method allows the exploitation of the temporal coverage provided by ERA-40 exceeding the lifetime of remote sensing instruments. Figure 11 shows a 44-year average of zonally averaged transfer velocities on a seasonal basis calculated using W′92. The average global net flux calculated from these transfer velocities using ΔpCO2 values by Takahashi et al.  is −2.01 Gt C/a ± 0.14 Gt C/a, excluding the diurnal-warming, cool-sea-surface-skin, atmospheric stability and shelf sea CO2 uptake effects discussed in section 3.1. A shorter-term average calculated from corrected AMSR-E data (2003–2004) is slightly lower than this estimate (−1.85 Gt C/a ± 0.10 Gt C/a) while QuikSCAT results lie between these values (−1.96 Gt C/a ± 0.07 Gt C/a) for the 5-year period 2000–2004. Discrepancies between these values are purely based on different temporal coverage of wind speed and SST data sets and remaining uncertainties in wind speed, since all results are based on the same fields of ΔpCO2, SST, and k-parameterizations.
 A 44-year time series of global mean transfer velocity and net air-sea flux of carbon dioxide calculated from corrected ERA-40 wind speed data is shown in Figure 12.
 Our results show that discrepancies in both monthly mean values and representation of submonthly variability between wind speed data from different remote sensing and model sources are significant for the calculation of the marine CO2 budget on regional and global scales. As established for earlier data sets by, e.g., Boutin et al.  and Carr et al. , none of the currently available data sources provide ideal sampling conditions.
 We have shown that current techniques aimed at the parameterization of submonthly variability yield different results when applied to different data sets. It is therefore unlikely that a set of independent universal correction factors could be obtained that are applicable to monthly mean wind data on a general basis.
 Our methodology of correcting monthly means to a scatterometer-like standard before applying scatterometer-derived correction factors for submonthly variability is somewhat crude but points in a promising direction. The regression of zonally integrated monthly means from different sensors produces good results and the obtained transfer velocities and gas fluxes agree to within approximately 1% and 10%, respectively. Given the fact that (1) the time coverage of the different data sets does not always overlap (in particular AMSR-E and ERA-40 which differ by the greatest amount) (2) we are comparing 2-year averages with 44-year averages and (3) we have significantly reduced spatiotemporal coverage of our correction factors, this agreement is remarkable. Nevertheless, remaining discrepancies such as the winter transfer velocities in the high-latitude northern hemisphere observed in ERA-40 data indicate more fundamental differences between the data sets which cannot be accounted for by a simple regression between monthly means. This raises some concerns as to the accuracy of our results on a regional basis which should be addressed in future studies.
 Zonally integrated profiles of transfer velocity illustrate the role of the high-latitude oceans as regions of significant CO2 uptake due to high values of k, exceeding 30 cm/h in seasonal average. Likewise, the tropical oceans, known to be a major source of outgassing exhibit very low transfer velocities just over 10 cm/h in seasonal average indicating the impact of the strong air-sea concentration gradients of CO2 in these regions.
 The time series of transfer velocity and net air-sea CO2 flux over 44 years shown in Figure 12 illustrates the interannual and decadal variability based on global variations of wind speed (note that applied ΔpCO2 fields were assumed to be constant between years). It indicates significantly higher global transfer velocities and oceanic uptake of CO2 in 1980–2000 compared to 1960–1980 with relative differences of approximately 1.1 cm/h and 0.2 Gt C/a, respectively. It is unclear if such a change in flux really occurred since interannual changes in ΔpCO2 are unknown at present and are neglected in this study. However, a similar trend was observed in a long-term model study by Wetzel et al. . With respect to both transfer velocity and CO2 flux, pre-1980 values are expected to be less accurate as a result of greater uncertainties in the ERA-40 data, predominantly in the Southern hemisphere. Wetzel et al.  assign the trend to a strengthening of forcing winds predominantly in the Southern Hemisphere but their results are subject to the same uncertainty since their model is forced by NCEP/NCAR winds.
 A significant diversity in CO2 flux resulting from calculations based on wind data from a scatterometer (QuikSCAT), a passive microwave sensor (AMSR-E) and a model reanalysis (ERA-40) demonstrates the care necessary to determine air-sea exchange of CO2 accurately. We have shown that compared to QuikSCAT, both AMSR-E and ERA-40 underestimate wind speeds over most of the spectrum but particularly at high winds which are important for calculations of transfer velocity. Furthermore, unlike spatial resolution which is of lesser importance, there is a need for the parameterization of temporal variability of wind speeds. This parameterization needs to go beyond the simple assumption that wind speeds are Rayleigh distributed but should ideally be less complex than the computation of correction factors pixel by pixel for each month which are unique for each sensor. Note also that many data sources are anyway inadequate as they poorly represent the true distribution of wind speeds. No data source is ideal in this respect but QuikSCAT presents the most credible source of reliable wind speed distributions.
 We have shown a simple method to develop seasonally and zonally varying correction factors for the parameterization of submonthly variability of wind speed and to correct monthly mean wind data in such a way that it has properties equivalent to those of QuikSCAT. The error introduced by the reduction of spatial and temporal complexity of the correction factors is small compared to other uncertainties involved.
 Then, the correction factors parameterizing temporal variability derived from QuikSCAT are applied to the corrected monthly means from QuikSCAT, AMSR-E, and ERA-40. The result is a unification of global gas transfer velocities calculated from different wind data sources giving a significantly more coherent picture of global air-sea CO2 flux. Furthermore, it opens the door to several decades of model reanalysis data which can now be used to obtain long-term averages of global gas transfer velocities and allow the analysis of interannual variability of transfer velocity on decadal scales.
 In the future, an increasing level of overlap between remotely sensed data from various sensors is likely to increase the accuracy of this methodology. Discrepancies between data sets will be better understood which allows a more systematic correction of the monthly mean wind speeds. However, for the time being we have shown a successful first attempt to reduce variability between different wind data sets and to unify the resulting scattered values of transfer velocities and net air-sea CO2 transfer currently found in the literature. It should be noted however that further uncertainty as a result of ΔpCO2, SST and parameterization of transfer velocity were not addressed in this work.
 A 44-year average derived from corrected ERA-40 data gives a global mean transfer velocity of 20.8 cm/h ± 0.7 cm/h and a global net flux of −2.01 Gt C/a ± 0.14 Gt C/a (using W′92), excluding the effects of diurnal warming, the cool sea surface skin as well as contributions by shelf seas.
 QuikSCAT data were produced by Remote Sensing Systems and sponsored by the NASA Ocean Vector Winds Science Team. AMSR-E data were produced by Remote Sensing Systems and sponsored by the NASA Earth Science REASoN DISCOVER Project and the AMSR-E Science Team. Both data sets are available at www.remss.com. ERS data were obtained from CERSAT, Ifremer, Plouzané (France) and are available at www.ifremer.fr/cersat. ERA-40 data were produced by ECMWF and are available at www.ecmwf.int; the authors would like to thank Sofia Caires and Andreas Sterl for their advice on ERA-40 data. HadISST data were provided by the Hadley Centre, Met Office, UK. They were obtained from the British Atmospheric Data Centre (BADC) website at http://badc.nerc.ac.uk/data/hadisst/. This work was funded by the NERC Centre for the observation of Air-Sea Interaction and fluXes (CASIX), CASIX publication no. 49.