17 Generic Utilities & Functions

17.0.1 Gas Transfer

This section descrives some popularly used gas exchange velocity that are optionally selcted in various AED modules. The key factors of wind speed, current speed, and water depths are considered.

When choosing an algorithm, consider the following selection criteria:

  1. Environment: ocean; lake; estuary/river;
  2. Study for which gas: O2, CH4, N2O, CO2
  3. Variables: wind speeds (\(U\)), current speeds (\(v\)), depths (\(h\))
  4. Schmidt number normalization: yes/no. \(Sc = \frac{\mu }{d} = \frac{\text{kinematic viscosity}}{\text{diffusion}}\)


Table 17.1: Options for schmidt number calculation in gas-exchange calculations.
Source Computation AED Case Number
\(schmidt = (0.9+0.1*\frac{salt}{35.0})*(1953.4+temp*(-128.0+temp*(3.9918-temp*0.050091)))\) 1
\(schmidt = 0.9 + \frac{salt}{350.0}\)
\(schmidt = schmidt * (2073.1 -125.62*temp +3.6276*temp^{2} - 0.043219*temp^{3})\) 		2
\(schmidt = (1.0 + 3.4e-3*salt)\)
\(schmidt = schmidt * (1800.6 -120.1*temp +3.7818*temp^{2} - 0.047608*temp^{3})\) 		3
Arianto Santoso \(schmidt = 2039.2 - (120.31*temp) + (3.4209*temp^{2}) - (0.040437*temp^{3})\)
\(schmidt = \frac{schmidt}{600}\) 		4
Wanninkhof (1992) \(schmidt = 1897.8 - (114.28*temp) + (3.2902*temp^{2}) - (0.039061*temp^{3})\) 5
Wanninkhof (1992) \(schmidt = 2055.6 - (137.11*temp) + (4.3173*temp^{2}) - (0.054350*temp^{3})\) 6

Table 17.2: Options for gas exchnage velocity calculation.
Source Computation
\(v\): current velocity
\(U\): wind speed
\(h\): water depth 		Environment Gas Required Variables \(Sc\) Normalisation Comment AED Option Number
Liss and Merlivat (1986) \(k = K_{600}(\frac{Sc}{600})^{-\frac{1}{2}}\)
\(K_{600} = 0.17U\) for \(U \leq 3.6\)
\(K_{600} = 2.85U - 9.65\) for \(3.6 \lt U \leq 13\)
\(K_{600} = 5.9U - 49.3\) for \(U \gt 13\) 		Lake and ocean CO2 \(U\) Yes, 600 One of the most popular formulas in early stage \(\Theta_{gas}^{schmidt} = 1\)
Wanninkhof (1992) \(k = 0.31U^{2}(\frac{Sc}{660})^{-\frac{1}{2}}\) Ocean, open lakes CO2 \(U\) Yes, 660 One of the most globally popular formulas for oceans and lakes \(\Theta_{gas}^{schmidt} = 2\)
Wanninkhof (2014) \(k = 0.251U^{2}(\frac{Sc}{660})^{-\frac{1}{2}}\) Ocean, open lakes CO2 \(U\) Yes, 660 Updated formula of Wanninkhof (1992). Note the coefficient of 0.251 is now closer to Ho et al. (2011), Ho et al. (2016), and Borges et al. (2004). \(\Theta_{gas}^{schmidt} = 3\)
Ho et al. (2011) \(k = 0.26U^{2}(\frac{Sc}{600})^{-\frac{1}{2}}\) Ocean, coastal area He/SF6 \(U\) Yes, 600 Measurement at ocean and coastal area \(\Theta_{gas}^{schmidt} = 4\)
Ho et al. (2016) \(k = K_{600}(\frac{Sc}{600})^{-\frac{1}{2}}\)
\(K_{600} = 0.77v^{\frac{1}{2}}h^{-\frac{1}{2}}+0.266U^{2}\) 		Estuary, rivers He/SF6 \(v\),\(U\),\(h\) Yes, 600 Measurement at estuarine environment \(\Theta_{gas}^{schmidt} = 5\)
Raymond and Cole (2001) \(k = K_{600}(\frac{Sc}{600})^{-\frac{1}{2}}\)
\(K_{600} = 1.91exp(0.35U)\) 		Estuary, rivers CO2 \(U\) Yes, 600 An equation for estuary/river environment but against only on winds based on extensive review. Note the K value here is much higher than ocean environment in high wind speeds (e.g. Wanninkhof (1992)). \(\Theta_{gas}^{schmidt} = 6\)
Borges et al. (2004) \(k = K_{600}(\frac{Sc}{600})^{-\frac{1}{2}}\)
\(K_{600} = 1.0 + 1.719v^{\frac{1}{2}}h^{\frac{1}{2}}+2.85U\) 		Scheldt Estuary CO2 \(v\),\(U\),\(h\) Yes, 600 A equation for estuary environment from extensive measurement at Scheldt Estuary \(\Theta_{gas}^{schmidt} = 7\)
Rosentreter et al. (2016) \(k = K_{600}(\frac{Sc}{600})^{-\frac{1}{2}}\)
\(K_{600CO_{2}} = -0.08+0.26v+0.83U+0.59h\)
\(K_{600CO_{4}} = -1.07+0.36v+0.99U+0.87h\) 		Estuaries CO2, CH4 \(v\),\(U\),\(h\) Yes, 600 Equations developed specially for Queensland estuaries \(\Theta_{gas}^{schmidt} = 8\)

References

Borges, A.V., Vanderborght, J.-P., Schiettecatte, L.-S., Gazeau, F., Ferrón-Smith, S., Delille, B., Frankignoulle, M., 2004. Variability of the gas transfer velocity of CO2 in a macrotidal estuary (the Scheldt), Estuaries 27, 593–603. https://doi.org/10.1007/bf02907647
Ho, D.T., Coffineau, N., Hickman, B., Chow, N., Koffman, T., Schlosser, P., 2016. Influence of current velocity and wind speed on air-water gas exchange in a mangrove estuary: Gas Exchange in a Mangrove Estuary, Geophysical Research Letters 43, 3813–3821. https://doi.org/10.1002/2016gl068727
Ho, D.T., Wanninkhof, R., Schlosser, P., Ullman, D.S., Hebert, D., Sullivan, K.F., 2011. Toward a universal relationship between wind speed and gas exchange: Gas transfer velocities measured with 3 He/SF 6 during the Southern Ocean Gas Exchange Experiment, Journal of Geophysical Research 116. https://doi.org/10.1029/2010jc006854
Liss, P.S., Merlivat, L., 1986. The Role of Air-Sea Exchange in Geochemical Cycling 113–127. https://doi.org/10.1007/978-94-009-4738-2\_5
Raymond, P.A., Cole, J.J., 2001. Gas Exchange in Rivers and Estuaries: Choosing a Gas Transfer Velocity, Estuaries 24, 312. https://doi.org/10.2307/1352954
Rosentreter, J.A., Maher, D.T., Ho, D.T., Call, M., Barr, J.G., Eyre, B.D., 2016. Spatial and temporal variability of CO 2 and CH 4 gas transfer velocities and quantification of the CH 4 microbubble flux in mangrove dominated estuaries: Gas transfers in estuaries, Limnology and Oceanography 62, 561–578. https://doi.org/10.1002/lno.10444
Wanninkhof, R., 2014. Relationship between wind speed and gas exchange over the ocean revisited: Gas exchange and wind speed over the ocean, Limnology and Oceanography: Methods 12, 351–362. https://doi.org/10.4319/lom.2014.12.351
Wanninkhof, R., 1992. Relationship between wind speed and gas exchange over the ocean, Journal of Geophysical Research 97, 7373. https://doi.org/10.1029/92jc00188