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Naval Research Laboratory (NRL)
Air-Sea Exchange Coefficients (NASEC)

U.S. Naval Research Laboratory, Stennis Space Center



1. Introduction

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).


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.

2. Stability-Dependent Exchange Coefficients

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 7C 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:

CD: Wind stress drag coefficient

CL: Latent heat flux coefficient

Ta: Air temperature at 10 m above the sea surface (C)

Ts: Sea surface temperature (C)

Va: Wind speed at 10 m above the sea surface (m/s)

RH: Relative humidity (%)


CAUTION: In the figures, CD and CL obtained from COARE3.0 are shown to consistently increase at higher wind speeds (>25 m/s). This is contrary to what such field projects, tank experiments and GPS profile data have shown. A constant value may be used for winds stronger than 25 m/s. By changing vamax in the fortran programs below from 40 m/s to (say) 25 m/s, CD and CL can be held constant for winds stronger than 25 m/s.

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


2.1. NASEC Algorithms 

The fortran programs to generate wind stress drag coefficient (CD) and latent heat flux coefficient (CL) are provided here.

cd_new_va.f : The NASEC algorithm to obtain CD based on air-sea stability.

cl_new_va.f : The NASEC algorithm to obtain CL based on air-sea stability.

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 CD over the global ocean.


2.2. COARE v3.0 

COARE 3.0 algorithms modified to output a table of transfer coefficients (i.e., wind stress drag coefficient and latent heat flux coefficient.).
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 CD and CL based upon various Ta-Ts.

Tabtem.F: The program providing CD and CL based upon various Va.


3. NASEC Exchange Coefficients

In this section, the exchange coefficients for CD and CL are provided in tabulated forms based on a wide range of Ta-Ts, Va 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 "CE" has changed to CL for the tables below.

To obtain the tabulated exchange coefficients, a Ts value of 10C was chosen because almost no sensitivity to the choice of Ts 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 30C and upwards.

3.1. Tabulated CD values based on Ta-Ts values:

TabcorXXX.CD where XXX is the relative humidity (%) at the air-sea interface.

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

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


3.2. Tabulated CD values based on Va values:

TabtemXXX.CD where XXX is the relative humidity (%) at the air-sea interface.

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

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


3.3. Tabulated CL values based on Ta-Ts values:

TabcorXXX.CL where XXX is the relative humidity (%) at the air-sea interface.

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

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

3.4. Tabulated CL values based on Va values:

TabtemXXX.CL where XXX is the relative humidity (%) at the air-sea interface.

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

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



4. Creeping Sea-Fill Methodology


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.


5. Air-Sea Algorithms and Their Abbreviations

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.


AbbreviationAir-Sea Flux AlgorithmFortan programsReference
COARECoupled Ocean-Atmosphere Response Experimenttoga_to10m.f90Fairall et al. (2003)
LKBLiu-Katsaros-Businger modeltoga_to10m_lkb.f90Liu and Tang (1996)
BVWBourassa-Vincent-Wood modeltoga_to10m_bvw.f90
Bourassa et al. (1999)
BVWNBourassa-Vincent-Wood neutral modeltoga_to10m_bvwn.f90Bourassa et al. (1999)
LOGLogarithmically varying profiletoga_to10m_LOG.f90Peixoto and Oort (1992)

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

6. Height Adjustment to 10 m

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.

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.obsOriginal daily buoy data
0n110w.10mAtmospheric variables adjusted to 10 m using COARE v3.0
0n110w.lkbAtmospheric variables adjusted to 10 m using LKB
0n110w.bvwAtmospheric variables adjusted to 10 m using BVW
0n110w.bvwnAtmospheric variables adjusted to 10 m using BVWN
0n110w.log.txtAtmospheric 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.obsOriginal daily buoy data
0n10w.10mAtmospheric variables adjuste to 10 m using COARE v3.0
0n10w.lkb Atmospheric variables adjusted to 10m using LKB
0n10w.bvwAtmospheric variables adjusted to 10 m using BVW
0n10w.bvwnAtmospheric variables adjusted to 10 m using BVWN
0n10w.log.txtAtmospheric 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.metOriginal hourly buoy data in 2005
10m_2005_hour_35n073w.metAdjusted to 10 m using COARE v3.0
lkb_2005_hour_35n073w.metAdjusted to 10 m using LKB
bvw_2005_hour_35n073w.metAdjusted to 10 m using BVW
bvwn_2005_hour_35n073w.metAdjusted to 10 m using BVWN
LOG_2005_hour_35n073w.metAdjusted 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.



7. References

Note: All publications are also available online: Go to Publications home page



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.
Click here to download

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



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