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).
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:
CAUTION: In the figures, C
D and C
L 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,
C
D and C
L can be held constant for winds stronger than 25 m/s.
2.1. NASEC Algorithms
The fortran programs to generate wind stress drag coefficient (C
D) and latent heat flux coefficient (C
L) are provided here.
cd_new_va.f : The NASEC algorithm to obtain C
D based on air-sea stability.
cl_new_va.f : The NASEC algorithm to obtain C
L 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 C
D 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 C
D and C
L based upon various T
a-T
s.
Tabtem.F: The program providing C
D and C
L based upon various V
a.
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 10°C 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
30°C 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.CDTabcor060.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.CDTabtem060.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.CLTabcor050.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.CLTabtem050.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.
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 exampleAir 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 exampleThe 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.
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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