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A Relationship between the Bowen Ratio and Sea–Air Temperature Difference under Unstable Conditions at Sea

S. A. Hsu Coastal Studies Institute, Louisiana State University, Baton Rouge, Louisiana

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Print Publication:
01 Nov 1998
DOI:
https://doi.org/10.1175/1520-0485(1998)028<2222:ARBTBR>2.0.CO;2
Page(s):
2222–2226
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Abstract

At the air–sea interface, estimates of evaporation or latent heat flux and the Monin–Obukhov stability parameter require the measurements of dewpoint (Tdew) or wet-bulb temperature, which are not routinely available as compared to those of air (Tair) and sea surface temperature (Tsea). On the basis of thermodynamic considerations, this paper first postulates that the quantity of (qsea − qair) for the difference in specific humidity between the sea surface and its overlying air is related to the quantity of (Tsea − Tair). Using hourly measurements of all three temperatures, that is, Tsea, Tair, and Tdew from a buoy in the Gulf of Mexico under a severe cold air outbreak, a linear correlation between (qsea − qair) and (Tsea − Tair) does exist with a compelling high correlation coefficient, r, of 0.98 between these two quantities. Second, based on this Clausius-Clapeyron effect, the Bowen ratio B is proposed to relate to the quantity of (Tsea − Tair) only such that B = a(Tsea − Tair)b. Using all data for these three temperatures available from four stations in the Gulf from 1993 through 1997 reveal that for deepwater a varies from 0.077 to 0.078, b from 0.67 to 0.71, and r from 0.85 to 0.89. Similar equations for the nearshore region are also provided. Limited datasets from the open ocean also support this generic relationship between B and the quantity of (Tsea − Tair).

Corresponding author address: Dr. S. A. Hsu, Coastal Studies Institute, 308 Howe-Russell Geoscience Bldg., Louisiana State University, Baton Rouge, LA 70803. E-mail: sahsu@antares.esl.lsu.edu

Abstract

At the air–sea interface, estimates of evaporation or latent heat flux and the Monin–Obukhov stability parameter require the measurements of dewpoint (Tdew) or wet-bulb temperature, which are not routinely available as compared to those of air (Tair) and sea surface temperature (Tsea). On the basis of thermodynamic considerations, this paper first postulates that the quantity of (qsea − qair) for the difference in specific humidity between the sea surface and its overlying air is related to the quantity of (Tsea − Tair). Using hourly measurements of all three temperatures, that is, Tsea, Tair, and Tdew from a buoy in the Gulf of Mexico under a severe cold air outbreak, a linear correlation between (qsea − qair) and (Tsea − Tair) does exist with a compelling high correlation coefficient, r, of 0.98 between these two quantities. Second, based on this Clausius-Clapeyron effect, the Bowen ratio B is proposed to relate to the quantity of (Tsea − Tair) only such that B = a(Tsea − Tair)b. Using all data for these three temperatures available from four stations in the Gulf from 1993 through 1997 reveal that for deepwater a varies from 0.077 to 0.078, b from 0.67 to 0.71, and r from 0.85 to 0.89. Similar equations for the nearshore region are also provided. Limited datasets from the open ocean also support this generic relationship between B and the quantity of (Tsea − Tair).

Corresponding author address: Dr. S. A. Hsu, Coastal Studies Institute, 308 Howe-Russell Geoscience Bldg., Louisiana State University, Baton Rouge, LA 70803. E-mail: sahsu@antares.esl.lsu.edu

1. Introduction

At the air–sea interface under unstable conditions when the sea is warmer than the air, the sensible heat flux Hs is defined as [see, e.g., Smith 1980, Eq. (4)]
HsρCpCTTseaTairU10
where ρ is the air density and Cp the specific heat capacity at constant pressure, Tsea is the “bucket” seawater temperature in the wave-mixed layer, Tair is the mean air temperature at the 10-m reference height, CT is the sensible heat flux coefficient, and U10 is the wind speed at the 10-m reference height.
The latent heat flux Hl is defined as (Roll 1965)
HlLTELTCEρqseaqairU10
where LT is the latent heat of vaporization, E is the evaporation, CE is the latent heat flux coefficient, and qsea and qair are the specific humidity for the sea and air, respectively.
Since the total heat flux requires the addition of Hs and Hl and since values of q need the input of vapor pressure, which is not always measured, the so-called Bowen ratio B has been suggested (see, e.g., Roll 1965) and from Eqs. (1) and (2), we have
i1520-0485-28-11-2222-e3
where B may vary from 0.1 to 0.3 in the Tropics (e.g., Pond et al. 1971) and from 0.61 to 0.78 during cold air outbreaks over a midlatitude coastal water (Chou et al. 1986).

The Bowen ratio in the marine environment has been studied by many investigators (see, e.g., Roll 1965; Pond et al. 1971; Kondo 1976; Hicks and Hess 1977; Rao et al. 1986; Liu and Niiler 1990; Konda and Imasato 1996). The spatial variation of B is large, particularly for shallow seas during winter when cold air outbreaks occur frequently. An example is shown in Fig. 1. During the Air Mass Transformation Experiments (AMTEX) from 14–28 February 1974, in the sea areas of the southwest islands of Japan, the value of B was about 0.7–0.8 over the Yellow Sea, whereas it was 0.3–0.4 over the AMTEX region, and 0.1–0.2 over the subtropical Pacific Ocean. Kondo (1976) speculated that the saturation vapor pressure (es) is very low at low temperatures, but as the temperature increases, es increases exponentially, so that the ratio of the sea–air vapor pressure difference to the sea–air temperature difference takes a large value for high temperatures. The main purpose of this research is to further substantiate this Clausius-Clapeyron effect physically and mathematically.

The total heat flux Htotal can be estimated from B and Hs and from Eq. (3),
i1520-0485-28-11-2222-e4
Also, in the atmospheric surface boundary layer the value of B is needed in order to compute the Monin–Obukhov stability length, which takes the form (see Panofsky and Dutton 1984, p. 132)
i1520-0485-28-11-2222-e5
where u∗ is the friction velocity, κa is the von Kármán constant, and g is the gravitational acceleration.

The objectives of this paper are 1) to offer a possible explanation regarding the variation of B based on thermodynamic considerations, 2) to formulate a relationship between (Tsea − Tair) and (qsea − qair), and 3) to develop a formula that relates B to (Tsea − Tair) only so that one may “bypass” the requirement of (qsea − qair) measurements.

2. Thermodynamic considerations

At the sea surface, the specific humidity qsea is related to the saturation vapor pressure esea through (see, e.g., Hsu 1988, pp. 20–21)
i1520-0485-28-11-2222-e6
where
esea = 6.1078 × 10[7.5Tsea/(237.3+Tsea)]
and p is the atmospheric pressure. Thus, qsea is related nonlinearly to Tsea.
Similarly,
i1520-0485-28-11-2222-e8
where
eair = 6.1078 × 10[7.5Tdew/(237.3+Tdew)]
in which Tdew is the dewpoint temperature in degrees Celsius. So, qair is related to Tdew nonlinearly.

The problem now is to find a relationship between Tdew and Tair so that qair can be related to Tair. This is accomplished as follows.

For the dry adiabatic lapse rate (see, e.g., Hsu 1988, pp. 23–24),
i1520-0485-28-11-2222-e10
where z is the altitude. In a well-mixed atmospheric boundary layer from surface to the lifting condensation level (LCL: Hsu 1988, pp. 26–27),
i1520-0485-28-11-2222-e11
where HLCL is the height of the LCL. For dewpoint lapse rate (see, e.g., McIlveen 1986, p. 151),
i1520-0485-28-11-2222-e12
where Rυ and R is the gas constant for water vapor and dry air, respectively. For typical low tropospheric Tdew between 283 K (or 10°C) and 293 K (or 20°C), Eq. (12) becomes approximately
i1520-0485-28-11-2222-e13
or
i1520-0485-28-11-2222-e14
At the LCL, Tdew LCL = TLCL, and Eqs. (14)–(11) become
i1520-0485-28-11-2222-e15
where HLCL is in meters and the dewpoint depression at the surface is in degrees Celsius.

Therefore, Tdew is linearly related to Tair near the sea surface through the parameterization of HLCL. From Eqs. (8), (9), and (16), it is inferred that qair is related nonlinearly to Tair so that the composite quantity of (qsea − qair) may also be related nonlinearly to that of (Tsea − Tair). A proof of this idea is done in the next section.

3. Field results

Before the field results shown in Fig. 2 are presented, a relationship between the quantity (qsea − qair) as a function of the quantity (Tsea − Tair) must be verified for the idea as discussed above. Between 18 and 22 December 1996, a severe cold air outbreak occurred over the northern Gulf of Mexico, producing a large range of both (qsea − qair) and (Tsea − Tair) as shown in Fig. 3. Hourly data for both Tair and Tdew were obtained for Buoy 42040. The results are plotted in Fig. 3. Two curves are obtained, one is linear and the other nonlinear. It can be seen that the linear correlation between (qsea − qair) and (Tsea − Tair), with a very high correlation coefficient (r = 0.98), is superior to the nonlinear one (r = 0.96). That is, the linear equation provided in Fig. 3 can directly account for r2 = (0.98)2 = 96.0% of the variability in (qsea − qair) using (Tsea − Tair) alone. This correlation is very compelling. If we accept that the linear correlation between (qsea − qair) and (Tsea − Tair) does exist, we may then infer from Eq. (3) that B is also related to (Tsea − Tair) only. In fact, this idea is verified in Fig. 4 using the same dataset and Eq. (3) for the same period shown in Fig. 3. In other words, we postulate that
BaTseaTairb
or
BAbTseaTair
where a and b need to be determined from field data. The results from all available pairs of B as obtained from Eq. (3) with CT = 1.1 × 10−3 (see Large and Pond 1982) and CE = 1.12 × 10−3 (Smith et al. 1994) versus (Tsea − Tair) are shown in Fig. 2. Values of a and b along with the correlation coefficient r from the linear regression of Eq. (17b) between B and (Tsea − Tair) are obtained as follows according to the curve numbers for buoy/station

  1. GDIL1, 1995–96: B = 0.087(Tsea − Tair)0.76 with r = 0.79

  2. GDIL1, 1996–97: B = 0.087(Tsea − Tair)0.72 with r = 0.77

  3. 42002, 1996–97: B = 0.077(Tsea − Tair)0.69 with r = 0.85

  4. 42019, 1993–94: B = 0.077(Tsea − Tair)0.71 with r = 0.89

  5. 42040, 1996–97: B = 0.077(Tsea − Tair)0.70 with r = 0.89

  6. 42002, 1995–96: B = 0.078(Tsea − Tair)0.67 with r = 0.87.

If one accepts these high correlation coefficient values between B and (Tsea − Tair), one may say that Eq. (17) is verified. Note that hourly data for these four locations for the period given in Fig. 2 were based on measurements provided by the National Data Buoy Center, and for brevity and comparison purposes each individual point from each hour is not plotted in Fig. 2. According to Breaker et al. (1998), uncertainties in the calculated values of specific humidity from these buoys were estimated and ranged between 0.27% and 2.1% of the mean values as compared to nearby ship reports. Note that these hourly buoy data are also available on the World Wide Web. Note also that although the transfer coefficient of CT and CE may vary with stability (e.g., Konda 1996, Table 2), according to Garratt (1992, pp. 101–104), at present CE = CH ≃ 1.1 × 10−3 (±15%) under near neutral conditions. This is supported most recently by DeCosmo et al. (1996) that CEN = CHN = 1.1 × 10−3 and by Fairall et al. (1996) that CE = 1.11 × 10−3. Futhermore, according to Smith (1988, pp. 15470), Friehe and Schmitt (1976) summarized eddy correlation data then available to find CE = 1.32 × 10−3, corresponding to CEN = 1.18 × 10−3; the difference between CE and CEN was within the 15% range as suggested by Garratt (1992). Therefore, we use CT = 1.1 × 10−3 based on Large and Pond (1982) and CE = 1.12 × 10−3 from Smith et al. (1994) for our computations.

The results as assembled in Fig. 2 are interesting in that for different years at different locations from shelf break to the deeper Gulf of Mexico shown by curves 3 through 6, variations of a are only between 0.077 and 0.078 and b between 0.67 and 0.69 along with r between 0.85 and 0.89. In the nearshore area as represented by GDIL1 (for Grand Isle, Louisiana), however, both a and b values are higher as shown by curves 1 and 2 due possibly to land effects.

In order to apply Eq. (17) to the deep ocean, Fig. 5 is provided. All data points from Pond et al. (1971) were incorporated except number 12 from the Oregon State University run, which was questionable, as noted by the authors. It is surprising that with only 19 data points the correlation coefficient reaches 0.84. If one accepts this high correlation between B and (Tsea − Tair), Eq. (17) is also applicable to the deep ocean; although coefficients a and b may vary, the generic relationship does exist. Certainly, more data are needed to further verify Eq. (17) to deep ocean conditions.

4. Conclusions

On the basis of thermodynamic considerations, it is postulated that the quantities of (qsea − qair) and (Tsea − Tair) are related. This postulation was verified during a severe cold air outbreak over the northern Gulf of Mexico under which large ranges of (qsea − qair) versus (Tsea − Tair) along with a very high-correlation coefficient of 0.98 were found. With this compelling correlation, we further postulate that the Bowen ratio B is also related to the quantity of (Tsea − Tair) such that B = a(Tsea − Tair)b. Based on simultaneous hourly measurements of all three temperatures, that is, of Tair, Tsea, and Tdew in the Gulf of Mexico at four stations from 1993 through 1997, we found that in the Gulf of Mexico, values of a varied from 0.077 to 0.078, b from 0.67 to 0.71, and correlation coefficient r from 0.85 to 0.89. Because curve 5 covers the range of (Tsea − Tair) from 0° to 18°C, it is recommended for operational use. Equations for the nearshore environment are also obtained. Limited data from the open ocean also support this generic relationship between B and (Tsea − Tair). Certainly, similar measurements are needed from other ocean basins to further substantiate our proposed formulas.

Acknowledgments

This study was supported in part by the Louisiana/Texas Shelf Physical Oceanography Program funded by the U.S. Minerals Management Service (MMS) under Contract 14-35-0001-30509 for work to be performed by the Texas A&M University System and subcontractors. The contents of this paper do not necessarily reflect the views or policies of the MMS.

REFERENCES

  • Breaker, L. C., D. B. Gilhousen, and L. D. Burroughs, 1998: Preliminary results from long-term measurements of atmospheric moisture in the marine boundary layer in the Gulf of Mexico. J. Atmos. Oceanic Technol.,15, 661–676.

  • Chou, S.-H., D. Atlas, and E.-N. Yeh, 1986: Turbulence in a convective marine atmospheric boundary layer. J. Atmos. Sci.,43, 547–564.

  • DeCosmo, J., K. B. Katsaros, S. D. Smith, R. J. Anderson, W. A. Oost, K. Bumke, and H. Chadwick, 1996: Air–sea exchange of water vapor and sensible heat: The Humidity Exchange Over the Sea (HEXOS) results. J. Geophys. Res.,101 (C5), 12001–12016.

  • Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, 1996: Bulk parameterization of air–sea fluxes for Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment. J. Geophys. Res.,101 (C2), 3727–3764.

  • Friehe, C. A., and K. F. Schmitt, 1976: Parameterization of air–sea interface fluxes of sensible heat and moisture by the bulk aerodynamic formulas. J. Phys. Oceanogr.,6, 801–809.

  • Garratt, J. R., 1992: The Atmospheric Boundary Layer. Cambridge University Press, 316 pp.

  • Hicks, B. B., and G. D. Hess, 1977: On the Bowen ratio and surface temperature at sea. J. Phys. Oceanogr.,7, 141–145.

  • Hsu, S. A., 1988: Coastal Meteorology. Academic Press, 260 pp.

  • Konda, M., and N. Imasato, 1996: A new method to determine near-sea surface air temperature by using satellite data. J. Geophys. Res.,101 (C6), 14 349–14 360.

  • Kondo, J., 1976: Heat balance of the East China Sea during the Air Mass Transformation Experiment. J. Meteor. Soc. Japan,54, 382–398.

  • Large, W. G., and S. Pond, 1982: Sensible and latent heat flux measurements over the ocean. J. Phys. Oceanogr.,12, 464–482.

  • Liu, W. T., and P. P. Niiler, 1990: The sensitivity of latent heat flux to the air humidity approximations used in ocean circulation models. J. Geophys. Res.,96 (C6), 9745–9753.

  • McIlveen, J. F. R., 1986: Basic Meteorology. Van Nostrand Reinhold, 457 pp.

  • Panofsky, H. A., and J. A. Dutton, 1984: Atmospheric Turbulence. John Wiley, 397 pp.

  • Pond, S., G. T. Phelps, J. E. Paquin, G. McBean, and R. W. Stewart, 1971: Measurements of the turbulent fluxes of momentum, moisture and sensible heat over the ocean. J. Atmos. Sci.,28, 901–917.

  • Rao, G. R. L., M. V. Rao, P. H. Prasad, and K. G. Reddy, 1986: Distribution of Bowen ratio over the Indian Ocean. Mausam,37, 71–72.

  • Roll, H. U., 1965: Physics of the Marine Atmosphere. Academic Press, 426 pp.

  • Smith, S. D., 1980: Wind stress and heat flux over the ocean in gale force winds. J. Phys. Oceanogr.,10, 709–726.

  • ——, 1988: Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature. J. Geophys. Res.,93 (C12), 15 467–15 472.

  • ——, K. B. Katsaros, W. A. Oost, and P. G. Mestayer, 1994: The impact of the HEXOS programme. Preprints, Second Int. Conf. Air–Sea Interaction and on Meteorology and Oceanography of the Coastal Zone, Lisbon, Portugal, Amer. Meteor. Soc., 226–227.

Fig. 1.
Fig. 1.

The mean distribution of Bowen ratio for the entire period of AMTEX 1974 over the East China Sea region (after Kondo 1976).

Citation: Journal of Physical Oceanography 28, 11; 10.1175/1520-0485(1998)028<2222:ARBTBR>2.0.CO;2

Fig. 2.
Fig. 2.

Relationships between the Bowen ratio B and the quantity (Tsea − Tair) for the Gulf of Mexico (see text for explanation). The stations used are shown in the insert.

Citation: Journal of Physical Oceanography 28, 11; 10.1175/1520-0485(1998)028<2222:ARBTBR>2.0.CO;2

Fig. 3.
Fig. 3.

Relationships between (qsea − qair) and (Tsea − Tair) obtained from buoy 42040 (see Fig. 2 for location) during a cold air outbreak 18–22 December 1996. The mean, standard deviation, and the number of measurements are also provided in the figure.

Citation: Journal of Physical Oceanography 28, 11; 10.1175/1520-0485(1998)028<2222:ARBTBR>2.0.CO;2

Fig. 4.
Fig. 4.

The relationship between the Bowen ratio B and the quantity (Tsea − Tair) obtained from buoy 42040 (see Fig. 2 for location) during a cold air outbreak 18–22 December 1996. The mean, standard deviation, and number of measurements are also provided in the figure.

Citation: Journal of Physical Oceanography 28, 11; 10.1175/1520-0485(1998)028<2222:ARBTBR>2.0.CO;2

Fig. 5.
Fig. 5.

The relationship between the Bowen ratio B and the quantity (Tsea − Tair) for open ocean.

Citation: Journal of Physical Oceanography 28, 11; 10.1175/1520-0485(1998)028<2222:ARBTBR>2.0.CO;2

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  • Breaker, L. C., D. B. Gilhousen, and L. D. Burroughs, 1998: Preliminary results from long-term measurements of atmospheric moisture in the marine boundary layer in the Gulf of Mexico. J. Atmos. Oceanic Technol.,15, 661–676.

  • Chou, S.-H., D. Atlas, and E.-N. Yeh, 1986: Turbulence in a convective marine atmospheric boundary layer. J. Atmos. Sci.,43, 547–564.

  • DeCosmo, J., K. B. Katsaros, S. D. Smith, R. J. Anderson, W. A. Oost, K. Bumke, and H. Chadwick, 1996: Air–sea exchange of water vapor and sensible heat: The Humidity Exchange Over the Sea (HEXOS) results. J. Geophys. Res.,101 (C5), 12001–12016.

  • Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, 1996: Bulk parameterization of air–sea fluxes for Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment. J. Geophys. Res.,101 (C2), 3727–3764.

  • Friehe, C. A., and K. F. Schmitt, 1976: Parameterization of air–sea interface fluxes of sensible heat and moisture by the bulk aerodynamic formulas. J. Phys. Oceanogr.,6, 801–809.

  • Garratt, J. R., 1992: The Atmospheric Boundary Layer. Cambridge University Press, 316 pp.

  • Hicks, B. B., and G. D. Hess, 1977: On the Bowen ratio and surface temperature at sea. J. Phys. Oceanogr.,7, 141–145.

  • Hsu, S. A., 1988: Coastal Meteorology. Academic Press, 260 pp.

  • Konda, M., and N. Imasato, 1996: A new method to determine near-sea surface air temperature by using satellite data. J. Geophys. Res.,101 (C6), 14 349–14 360.

  • Kondo, J., 1976: Heat balance of the East China Sea during the Air Mass Transformation Experiment. J. Meteor. Soc. Japan,54, 382–398.

  • Large, W. G., and S. Pond, 1982: Sensible and latent heat flux measurements over the ocean. J. Phys. Oceanogr.,12, 464–482.

  • Liu, W. T., and P. P. Niiler, 1990: The sensitivity of latent heat flux to the air humidity approximations used in ocean circulation models. J. Geophys. Res.,96 (C6), 9745–9753.

  • McIlveen, J. F. R., 1986: Basic Meteorology. Van Nostrand Reinhold, 457 pp.

  • Panofsky, H. A., and J. A. Dutton, 1984: Atmospheric Turbulence. John Wiley, 397 pp.

  • Pond, S., G. T. Phelps, J. E. Paquin, G. McBean, and R. W. Stewart, 1971: Measurements of the turbulent fluxes of momentum, moisture and sensible heat over the ocean. J. Atmos. Sci.,28, 901–917.

  • Rao, G. R. L., M. V. Rao, P. H. Prasad, and K. G. Reddy, 1986: Distribution of Bowen ratio over the Indian Ocean. Mausam,37, 71–72.

  • Roll, H. U., 1965: Physics of the Marine Atmosphere. Academic Press, 426 pp.

  • Smith, S. D., 1980: Wind stress and heat flux over the ocean in gale force winds. J. Phys. Oceanogr.,10, 709–726.

  • ——, 1988: Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature. J. Geophys. Res.,93 (C12), 15 467–15 472.

  • ——, K. B. Katsaros, W. A. Oost, and P. G. Mestayer, 1994: The impact of the HEXOS programme. Preprints, Second Int. Conf. Air–Sea Interaction and on Meteorology and Oceanography of the Coastal Zone, Lisbon, Portugal, Amer. Meteor. Soc., 226–227.

  • Fig. 1.
    View in gallery
    Fig. 1.

    The mean distribution of Bowen ratio for the entire period of AMTEX 1974 over the East China Sea region (after Kondo 1976).

  • Fig. 2.
    View in gallery
    Fig. 2.

    Relationships between the Bowen ratio B and the quantity (Tsea − Tair) for the Gulf of Mexico (see text for explanation). The stations used are shown in the insert.

  • Fig. 3.
    View in gallery
    Fig. 3.

    Relationships between (qsea − qair) and (Tsea − Tair) obtained from buoy 42040 (see Fig. 2 for location) during a cold air outbreak 18–22 December 1996. The mean, standard deviation, and the number of measurements are also provided in the figure.

  • Fig. 4.
    View in gallery
    Fig. 4.

    The relationship between the Bowen ratio B and the quantity (Tsea − Tair) obtained from buoy 42040 (see Fig. 2 for location) during a cold air outbreak 18–22 December 1996. The mean, standard deviation, and number of measurements are also provided in the figure.

  • Fig. 5.
    View in gallery
    Fig. 5.

    The relationship between the Bowen ratio B and the quantity (Tsea − Tair) for open ocean.

Fig. 1.

The mean distribution of Bowen ratio for the entire period of AMTEX 1974 over the East China Sea region (after Kondo 1976).
Fig. 2.

Relationships between the Bowen ratio B and the quantity (Tsea − Tair) for the Gulf of Mexico (see text for explanation). The stations used are shown in the insert.
Fig. 3.

Relationships between (qsea − qair) and (Tsea − Tair) obtained from buoy 42040 (see Fig. 2 for location) during a cold air outbreak 18–22 December 1996. The mean, standard deviation, and the number of measurements are also provided in the figure.
Fig. 4.

The relationship between the Bowen ratio B and the quantity (Tsea − Tair) obtained from buoy 42040 (see Fig. 2 for location) during a cold air outbreak 18–22 December 1996. The mean, standard deviation, and number of measurements are also provided in the figure.
Fig. 5.

The relationship between the Bowen ratio B and the quantity (Tsea − Tair) for open ocean.
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