Relating air-sea gas transfer velocities, k, to wind speed, U
Several attempts have been made to relate air-sea gas transfer velocities, k, to wind speed, U. Relating k to U is not completely satisfactory because k is known to be driven by sea surface roughness which is not only dependent on wind speed and alternative approaches attempt to relate k to sea surface slopes (Frew et al., 2004) that is accessible using dual-frequency altimeters. However, scatterometer instruments provide a much better spatial coverage than altimeters.
At present, three k-U relationships are commonly used to derive CO2 air-sea fluxes from wind speed and air-sea CO2 partial pressure gradient:
- The Liss and Merlivat (1986) relationship deduced from process studies in wind tunnel and calibrated with lake measurements.
- TheWanninkhof (1992) relationship deduced by assuming (1) k is proportionnal to U2, (2) the global distribution of U is a Rayleigh distribution and (3) the global k average is constrained by the Broecker et al. (1985) ocean 14C inventory (Kbroecker).
- The Nightingale et al. (2000) relationship deduced from in situ tracer measurements (SF6,3He) performed at sea and assuming a second order polynomial k-U relationship.
As expected from older studies, global mean K values deduced from these 3 k-U relationships are quite stable temporally (no seasonal cycle) but the K deduced from various relationships disagree by up to a factor 1.8 and this factor varies regionally (Boutin et al., 2002).
Liss and Merlivat
The Liss and Merlivat  parameterisation was deduced, taking into account the physics of the air-sea interface, from wind tunnel measurements. Lake measurements were used for normalisation. It is divided in three regimes, smooth surface, rough surface and breaking waves regimes:
0<=U<=3.6m/s k[LM]=(0.17*U10)* (600./Sc)**0.66 3.6<U10<=13m/s k[LM]=((2.85*U10) - 9.65)*(600./Sc)**0.5 13<U10 k[LM]=((5.9*U10) - 49.3)*(600./Sc)**0.5
The Nightingale et al.  parameterisation was deduced from dual tracers experiments at sea:
k[N]=(0.222U10**2 + 0.333U10) * (600/Sc)**0.5
The Wanninkhof  parameterisation used a quadratic fit to the bomb 14C inventory. Since we use high resolution satellite wind speeds, we choose the parametrisation suitable for short term wind speed:
kW=(0.31 U10**2)* (660/Sc)**0.5
Computing K fields
In order to correctly take into account the non-linearity of the k-U relationships in the K averages, K is computed for each U10 retrieved at 25km resolution from instantaneous 25km scatterometer measurement; gas solubility and Schmidt number are computed for a constant salinity of 35 and for a sea surface temperature, SST, averaged over 1° and 1 month. The SST fields are the ones generated at the National Meteorological Center (NMC) by an optimal interpolation of AVHRR and in situ data [Reynolds and Smith .
Then, the 25km K estimates are interpolated on weekly and monthly 1° resolution grids using a kriging method described in [Bentamy et al., 1996]. Comparison between fields interpolated using this kriging method and the objective analysis described in [Boutin and Etcheto, 1995] shows differences inside the variability of wind speed within two satellite passages.
Global K weighted averages are deduced from monthly K maps from 1999 to 2006 as shown here. As expected from older studies, global mean K values deduced from these 3 k-U relationships are quite stable temporally (no seasonal cycle) but the K deduced from various relationships disagree by up to a factor 1.8 and this factor varies regionally (Boutin et al., 2002). Wanninkhof (1992) calibrated his k-U relationship on K deduced by Broecker et al., 1985 from Geosecs ocean 14C inventory: this corresponds to a mean K of 0.064 mol m-2 yr-1 matm-1 (Kbroecker); in addition Wanninkhof (1992) assumed a Rayleigh distribution of U with global mean U=7.4m/s. In fact, the QSCAT wind speed is on global average 7.8m/s (the discrepancy being possibly partly due to slight overestimate of QSCAT wind speeds) and does not exactly follow a Rayleigh distribution so that global Kw are on average 5% higher than the mean value assumed by Wanninkhof (1992) to calibrate his relationship.
Recently, new estimates of 14C ocean inventory have been proposed, either based on stratospheric modelling and/or analysis of WOCE data and/or reanalysis of Geosecs data:
- Hesshaimer et al. (1994) => Broecker Geosecs 14C inventory too high by 25%
- Peacock (2004) =>Revisited Geosecs inventory lower than Broecker by about 15%
- Naegler et al (2006) =>Revisited 14C inventory lower than Broecker by 12-20%
On global average, Kw, is 20% higher than the one derived with the Nightingale relationship, Kn; Kn are 15% lower than Kbroecker, in better agreement with Peacock (2004) and Naegler et al. (2005) new revisited inventory.
Bentamy, A., Y. Quilfen, F. Gohin, N. Grima, M. Lenaour, and J. Servain, Determination and validation of average wind fields from ERS-1 scatterometer measurements, The Global Atmosphere and Ocean System, 4, 1-29, 1996.
Boutin, J., and J. Etcheto, Estimating the chemical enhancement effect on the air-sea CO2 exchange using the ERS1 scatterometer wind speeds, in Air-Water Gas Transfer, edited by B.J.a.E.C. Monahan, pp. 827-841, AEON Verlag & Studio, Hanau, Germany, 1995.
Reynolds, R.W., and T.M. Smith, Improved global sea surface temperature analyses using optimum interpolation, Journal of Climate, 7, 929-948, 1994.