Naval Research Laboratory (NRL)

Air-Sea Exchange Coefficients (NASEC)

- 1. Introduction
- 2. Stability-Dependent Exchange Coefficients
- 3. NASEC Exchange Coefficients
- 4. Creeping Sea-Fill Methodology
- 5. Air-Sea Algorithms and Their Abbreviations
- 6. Height Adjustment to 10 m
- 7. References

Exchange coefficients for wind stress, latent and sensible heat fluxes,
were developed at the Naval Research Laboratory (NRL). These so-called
NRL Air-Sea Exchange Coefficients (NASEC) include stability
dependence through air-sea temperature difference, wind speed at 10
m above the sea surface and relative humidity.

Exchange Coefficients are first obtained from the Coupled Ocean-Atmosphere Response Experiment (COARE) bulk algorithm (version 3.0) as described in Fairall et al. (2003). They are then expressed as polynomial functions using simple fortran programs (Kara et al. 2005). That study is also an update of results presented Kara et al. (2000, 2002). Tabulated exchange coefficients based on various stability conditions are provided on this site. Two fortran programs generating these exchange coefficients are also made available.

The impact of ocean surface currents and surface waves are not taken into account in the NASEC algorithms. Such issues are further discussed over the global ocean (Kara et al. 2007a). Updated programs, including effects of ocean currents and waves on the exchange coefficients, are available below (see NASEC algorithms).

Spatial and temporal variations of wind stress drag coefficient are discussed over the global ocean (Kara et al. 2007b). In particular, monthly mean maps are provided from 1998 through 2004. As examples, here we show long term monthly (February and August) means of drag coefficients calculated using high temporal resolution (6 hourly) surface atmospheric variables (air-sea temperature difference, wind speed at 10 m and relative humidity at the air-sea interface) from European Centre for Medium-Range Weather Forecasts~(ECMWF) 40-year Re-Analysis (ERA-40) data. These two figures clearly reveal that in addition to spatial variations, drag coefficient has seasonal variability over the global ocean. Individual monthly mean plots of drag coefficient (i.e., inter-annual variations) can be found in Kara et al. (2007b).

Exchange Coefficients are first obtained from the Coupled Ocean-Atmosphere Response Experiment (COARE) bulk algorithm (version 3.0) as described in Fairall et al. (2003). They are then expressed as polynomial functions using simple fortran programs (Kara et al. 2005). That study is also an update of results presented Kara et al. (2000, 2002). Tabulated exchange coefficients based on various stability conditions are provided on this site. Two fortran programs generating these exchange coefficients are also made available.

The impact of ocean surface currents and surface waves are not taken into account in the NASEC algorithms. Such issues are further discussed over the global ocean (Kara et al. 2007a). Updated programs, including effects of ocean currents and waves on the exchange coefficients, are available below (see NASEC algorithms).

Spatial and temporal variations of wind stress drag coefficient are discussed over the global ocean (Kara et al. 2007b). In particular, monthly mean maps are provided from 1998 through 2004. As examples, here we show long term monthly (February and August) means of drag coefficients calculated using high temporal resolution (6 hourly) surface atmospheric variables (air-sea temperature difference, wind speed at 10 m and relative humidity at the air-sea interface) from European Centre for Medium-Range Weather Forecasts~(ECMWF) 40-year Re-Analysis (ERA-40) data. These two figures clearly reveal that in addition to spatial variations, drag coefficient has seasonal variability over the global ocean. Individual monthly mean plots of drag coefficient (i.e., inter-annual variations) can be found in Kara et al. (2007b).

Mean wind stress drag coefficient (x 0.001) in February | Mean wind stress drag coefficient (x 0.001) in August |

The NASEC exchange coefficients are suitable for a wide range of air-sea
interaction studies. Because they include full stability, they can be used
for studies dealing with not only long time (e.g., monthly, climatological)
but also short time (e.g., diurnal) scales.
The NASEC algorithms are computationaly inexpensive (does not require any
iteration), therefore, they are suitable for OGCM,
and coupled atmosphere-ocean model studies. For example, HYbrid Coordinate
Ocean Model (HYCOM) uses exchange coefficients from the NASEC algorithm. For the Ocean Model Intercomparison Project (OMIP)
forcing at the Max-Planck Institute for Meteorology, the turbulent heat
fluxes are also calculated using the exchange coefficients from NASEC.
If you are also using them, please let us know, so that we can add
here.

Exchange coefficients for wind stress and latent heat flux are
applicable to the wide range of conditions occurring over the global ocean: Wind speed from 1 to 40 m/s, air-sea
temperature difference intervals of -8 to 7°C and relative humidity values
of 0 to 100%.

The plots of exchange coefficients presented below are obtained for humidity close to or at saturation (i.e., RH=100%). Posted under the title "NASEC Exchange Coefficients" further below, the impact of various RH values on the exchange coefficients are provided in the tabulated forms.

Symbols used throughout the web page are described here:

The plots of exchange coefficients presented below are obtained for humidity close to or at saturation (i.e., RH=100%). Posted under the title "NASEC Exchange Coefficients" further below, the impact of various RH values on the exchange coefficients are provided in the tabulated forms.

Symbols used throughout the web page are described here:

CAUTION: In the figures, C

Wind stress drag coefficient with wind speed | Latent heat flux coefficient with wind speed |

Wind stress drag coefficient with air-sea temperature difference | Latent heat flux coefficient with air-sea temperature difference |

cd_new_va.f : The NASEC algorithm to obtain C

cl_new_va.f : The NASEC algorithm to obtain C

strblk_coare3.0.f : The NASEC algorithm to obtain wind stresses based on air-sea stability over the global ocean.

wind-wave-current.f : The NASEC algorithm involving effects of ocean currents and waves on C

Results from these algorithms are used for coding cd_new_va.f and cl_new_va.f above.

Module.F: The COARE module algorithm.

Tabcor.F: The program providing C

Tabtem.F: The program providing C

In this section, the exchange coefficients for C_{D} and C_{L} are provided in
tabulated forms based on a wide range of T_{a}-T_{s}, V_{a}
and RH values.
Note that all values in these tables must be multiplied by 0.001 (i.e,
1.0E-3). Note: The exchange coefficients are obtained in Tabcor.F and
Tabtem.F as provided above. In these, programs, the notation "C_{E}" has changed to C_{L} for
the tables below.

To obtain the tabulated exchange coefficients, a T_{s} value of 10°C was chosen
because almost no sensitivity to the choice of T_{s} was found. This is true since the only effect of the
temperature in the COARE algorithm enters through the non-linearity of
the saturation vapor pressure for water vapor which has some effect at
30°C and upwards.

To obtain the tabulated exchange coefficients, a T

Tabcor010.CD Tabcor020.CD Tabcor030.CD Tabcor040.CD Tabcor050.CD

Tabcor060.CD Tabcor070.CD Tabcor080.CD Tabcor090.CD Tabcor100.CD

Tabtem010.CD Tabtem020.CD Tabtem030.CD Tabtem040.CD Tabtem050.CD

Tabtem060.CD Tabtem070.CD Tabtem080.CD Tabtem090.CD Tabtem100.CD

Tabcor000.CL Tabcor010.CL Tabcor020.CL Tabcor030.CL Tabcor040.CL

Tabcor050.CL Tabcor060.CL Tabcor070.CL Tabcor080.CL Tabcor090.CL Tabcor100.CL

Tabtem000.CL Tabtem010.CL Tabtem020.CL Tabtem030.CL Tabtem040.CL

Tabtem050.CL Tabtem060.CL Tabtem070.CL Tabtem080.CL Tabtem090.CL Tabtem100.CL

Near--surface atmospheric variables from the uniformly gridded global
NWP products (e.g., ECMWF and NCEP) are generally at a spatial scale too
coarse to appropriately define the contrast between water and land grid points.
For example, ERA-40 has a longitudinal grid resolution of 1.125 degrees
and the NCEP Re-analysis has a longitudinal grid resolution of 1.875 degrees.

Atmospheric variables, such as, wind speed at 10 m, air temperature and relative humidity at 2 m, etc, from such NWP products are not quite accurate near the land-sea boundaries. As an example, the gridded products may have only one wind speed value near the coast, and it may not be clear if this value is representative of land or ocean. This single wind speed value can be influenced by both land and sea effects. In other words, there is land (sea) contamination over the sea (land) grid points near the coastal regions.

A creeping sea-fill methodology is presented to reduce land contamination for offshore applications (Kara et al. 2007c). NWP products provide land-sea mask fields, including 0's and 1's. In the case of ERA-40, fractional values (i.e., between 0 and 1) are given. Using this land-sea mask, the creeping sea-fill methodology makes use of only over-sea values of any given scalar atmospheric variable (e.g., wind speed at 10 m) and replaces the value associated with each land-masked point by one using only nearby sea values. Land-sea mask fields from NWP products (e.g., ERA-40, NCEP, NOGAPS) are available upon request. An application of the creeping sea-fill methodology can be seen from Kara et al. (2008a).

landfill.f : Subroutines for creeping sea-fill extrapolation

The subroutines landfill[125] extrapolate "ocean" (mask==1) values over "land" (mask==0), for 1, 2 or 5 independent fields (all with the same land/ocean mask), using multiple passes of a 9-point smoother based extrapolation scheme.

Atmospheric variables, such as, wind speed at 10 m, air temperature and relative humidity at 2 m, etc, from such NWP products are not quite accurate near the land-sea boundaries. As an example, the gridded products may have only one wind speed value near the coast, and it may not be clear if this value is representative of land or ocean. This single wind speed value can be influenced by both land and sea effects. In other words, there is land (sea) contamination over the sea (land) grid points near the coastal regions.

A creeping sea-fill methodology is presented to reduce land contamination for offshore applications (Kara et al. 2007c). NWP products provide land-sea mask fields, including 0's and 1's. In the case of ERA-40, fractional values (i.e., between 0 and 1) are given. Using this land-sea mask, the creeping sea-fill methodology makes use of only over-sea values of any given scalar atmospheric variable (e.g., wind speed at 10 m) and replaces the value associated with each land-masked point by one using only nearby sea values. Land-sea mask fields from NWP products (e.g., ERA-40, NCEP, NOGAPS) are available upon request. An application of the creeping sea-fill methodology can be seen from Kara et al. (2008a).

landfill.f : Subroutines for creeping sea-fill extrapolation

The subroutines landfill[125] extrapolate "ocean" (mask==1) values over "land" (mask==0), for 1, 2 or 5 independent fields (all with the same land/ocean mask), using multiple passes of a 9-point smoother based extrapolation scheme.

Moored
buoys measure surface atmospheric variables at various heights above
the sea surface. In most applications, one needs to adjust these
atmospheric variables to the standard height of 10 m, e.g., to
compute wind stress, latent and sensible heat fluxes. For this
purpose, as given in the following table, various air-sea algorithms
which can take full account of atmospheric stability in the near
surface layer in a simple or more complex way. In the case of winds,
some algorithms are also useful for determining neutral and
stability-dependent ones. This is especially useful for
converting equivalent neutral winds to the stability-dependent ones,
e.g., for those from the QuikSCAT satellite. All of these topics are discussed in Kara et al. (2008b).

Please note that in the table below we modified programs from their original sources for various applications, such as computing the near-surface air-sea stability, and thus adjusting atmospheric variables to the height at 10 m and determining neutral winds. The reader is referred to Kara at el. (2008b) for references and brief descriptions of the algorithms.

Please note that in the table below we modified programs from their original sources for various applications, such as computing the near-surface air-sea stability, and thus adjusting atmospheric variables to the height at 10 m and determining neutral winds. The reader is referred to Kara at el. (2008b) for references and brief descriptions of the algorithms.

Abbreviation | Air-Sea Flux Algorithm | Fortan programs | Reference |
---|---|---|---|

COARE | Coupled Ocean-Atmosphere Response Experiment | toga_to10m.f90 | Fairall et al. (2003) |

LKB | Liu-Katsaros-Businger model | toga_to10m_lkb.f90 | Liu and Tang (1996) |

BVW | Bourassa-Vincent-Wood model | toga_to10m_bvw.f90 | Bourassa et al. (1999) |

BVWN | Bourassa-Vincent-Wood neutral model | toga_to10m_bvwn.f90 | Bourassa et al. (1999) |

LOG | Logarithmically varying profile | toga_to10m_LOG.f90 | Peixoto and Oort (1992) |

Supplementary source codes, including implementation of each air-sea flux algorithm, can be found here.

Measurements
of ocean surface temperature, air temperature and relative humidity (or
specific humidity) are used for adjusting winds to 10~m from their
original heights and for calculating air--sea stability. Each buoy
provides a time series of near-surface atmospheric variables, with the
time period sampled in each record varying according to buoy
deployment duration and sensor operation. Using the air-sea flux
algorithms listed above, here we provide an example of adjusting hourly
surface atmospheric variables to the standard 10 m height a Tropical
Atmosphere-Ocean (TAO) buoy location, (0N,110W). At this
location, air temperature is measured at a height of 3.0 and and
wind speed is measured at a height of 4.0 m. In addition to the
adjustment to 10~m, we only compute mixing ratio values for air and sea.

Atmospheric variables at each buoy location are measured at various heights above the sea surface. Thus, heights of the sensors at TAO, PIRATA and NDBC stations used in our computations are also provided here.

Atmospheric variables at each buoy location are measured at various heights above the sea surface. Thus, heights of the sensors at TAO, PIRATA and NDBC stations used in our computations are also provided here.

tao_height.dat

pirata_height.dat

ndbc_height.dat

6.1. A TAO buoy example

Air temperature is measured at a height of 3.0 m and and wind speed is measured at a height of 4.0 m at this particular

buoy location. Results are shown for the historical data.

0n110w.obs | Original daily buoy data |

0n110w.10m | Atmospheric variables adjusted to 10 m using COARE v3.0 |

0n110w.lkb | Atmospheric variables adjusted to 10 m using LKB |

0n110w.bvw | Atmospheric variables adjusted to 10 m using BVW |

0n110w.bvwn | Atmospheric variables adjusted to 10 m using BVWN |

0n110w.log.txt | Atmospheric variables adjusted to 10 m using LOG |

Using each air-sea flux algorithm, similar adjustment processes are applied to all TAO buoys located in the equatorial Pacific Ocean.

Resulting files can be found here.

6.2. A PIRATA buoy example

Air temperature is measured at a height of 3.0 m and and wind speed is measured at a height of 4.0 m at this particular

buoy location. Results are shown for the historical data.

0n10w.obs | Original daily buoy data |

0n10w.10m | Atmospheric variables adjuste to 10 m using COARE v3.0 |

0n10w.lkb | Atmospheric variables adjusted to 10m using LKB |

0n10w.bvw | Atmospheric variables adjusted to 10 m using BVW |

0n10w.bvwn | Atmospheric variables adjusted to 10 m using BVWN |

0n10w.log.txt | Atmospheric variables adjusted to 10 m using LOG |

Using each air--sea flux algorithm, similar adjustment processes are applied to all PIRATA buoys located in the equatorial Atlantic Ocean.

Resulting files can be found here.

6.3. A NDBC buoy example

The NDBC buoy ID for this station is 41001, located at approximately 35N, 073W.

Air temperature is measured at a height of 4.0 m and and wind speed is measured at a height of 5.0 m.

In the example, at this buoy location we only show results in 2005.

obs_2005_hour_35n073w.met | Original hourly buoy data in 2005 |

10m_2005_hour_35n073w.met | Adjusted to 10 m using COARE v3.0 |

lkb_2005_hour_35n073w.met | Adjusted to 10 m using LKB |

bvw_2005_hour_35n073w.met | Adjusted to 10 m using BVW |

bvwn_2005_hour_35n073w.met | Adjusted to 10 m using BVWN |

LOG_2005_hour_35n073w.met | Adjusted to 10 m using LOG |

Using each air-sea flux algorithm, similar adjustment processes are applied to all NDBC buoys located at various regions of the global ocean. Resulting files can be found here.

Kara, A. B., C. N. Barron, A. J. Wallcraft, T. Oguz, and K. S. Casey, 2008a: Advantages of fine resolution SSTs for small ocean basins: Evaluation in the Black Sea J. Geophys. Res., 113, C08013, doi:10.1029/2007JC004569. Click here to download

Kara, A. B., A. J. Wallcraft, and M. A. Bourassa, 2008b: Air-sea stability effects on the 10m winds over the global ocean: Evaluations of air-sea flux algorithms. J. Geophys. Res., 113, doi:10.1029/2007JC004324. Click here to download

Kara, A. B., E. J. Metzger, and M. A. Bourassa, 2007a: Ocean current and wave effects on wind stress drag coefficient over the global ocean. Geophys. Res. Lett., 34, L01604, doi:10.1029/2006GL027849. Click here to download

Kara, A. B., A. J. Wallcraft, E. J. Metzger, H. E. Hurlburt, and C. W. Fairall, 2007b: Wind stress drag coefficient over the global ocean. J. Climate, 20, 5856-5864.

Kara, A. B., A. J. Wallcraft, and H. E. Hurlburt, 2007c: A correction for land contamination of atmospheric variables near land-sea boundaries. J. Phys. Oceanogr., 37, 803-818. Click here to download

Kara, A. B., H. E. Hurlburt, and A. J. Wallcraft, 2005: Stability-dependent exchange coefficients for air-sea fluxes. J. Atmos. Oceanic. Technol., 22, 1080-1094. Click here to download

Fairall, C. W., E. F. Bradley, J. E. Hare, A. A. Grachev, and J. B. Edson, 2003: Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm. J. Climate, 16, 571-591.

Kara, A. B., P. A. Rochford, and H. E. Hurlburt, 2002: Air-sea flux estimates and the 1997-1998 ENSO event. Bound. Layer Meteor., 103, 439-458. Click here to download

Kara, A. B., P. A. Rochford, and H. E. Hurlburt, Efficient and accurate bulk parameterizations of air-sea fluxes for use in general circulation models, 2000: J. Atmos. Oceanic Technol., 17, 1421-1438. Click here to download

Back to Oceanography Division home page

Back to Ocean Dynamics and Prediction home page

Back to NRL-SSC home page

Last revised: Thu Jul 30 11:49:56 CDT 2009