C. Fairall (NOAA/ERL)
E.F. Bradley (CSIRO)
D. Rogers (Scripps)


In 1993, Chris Fairall, Frank Bradley and David Rogers began development of a bulk air-sea flux algorithm for use by the COARE community. Based on the model of Liu, Katsaros and Businger (1979, LKB), it took account of the light wind, strongly convective conditions over tropical oceans. Version 1.0 was released in November 1993, and included modifications to the basic LKB code for wind roughness length (Smith, 1988), Monin-Obukhov profile functions for strong convection, and low-wind "gustiness" (Godfrey and Beljaars, 1991). Version 2.0 (August 1994) included code to model the cool skin physics (Saunders, 1967), and also daytime near-surface warming based on a simplified version of the Price, Weller and Pinkel (1986) ocean mixing model (Fairall et al., 1996a). These optional features enable conversion from bulk to true skin temperature for calculating the fluxes. Calculation of fluxes of momentum (Caldwell and Elliott, 1971) and sensible heat (Gosnell, Fairall and Webster, 1995) due to rainfall are incorporated in the code, as is the so-called Webb correction to latent heat flux which arises from the requirement that the net dry mass flux be zero (Webb et al., 1980). The formalism of the algorithm is fully described in Fairall et al. (1996b).

The last major modifications to the algorithm were made at the COARE Air-Sea Interaction (Flux) Group Workshop in Honolulu, 2-4 August 1995 (Bradley and Weller, 1995). Transfer coefficients were adjusted by six percent to give better average agreement with covariance latent heat fluxes from several COARE ships. This produced version 2.5b, which has been used successfully on various ocean-atmosphere field campaigns by members of the Flux Group, at various locations and from a variety of platforms. At the Woods Hole workshop, 9-11 October 1996 (Bradley and Weller, 1997) it was agreed that no further development would be attempted to the community version of the COARE Bulk Flux Algorithm, and that a version 2.5b bulk algorithm "package" would be made available, consisting of the fortran source code and a test data set. This was released at a meeting of the Flux Group at NCAR, 14-16 May 1997 (Bradley, Moncrieff and Weller, 1997):

Description of the bulk algorithm "package"

The "package" consists of three files:

coar2_5b.f 33K (Fortran source code)
test2_5b.dat 12K (Test data set)
test2_5b.out 14K (Output file from test data)

Fortran program

A full description of the code and the test data set appears at the head of the fortran file. We provide some notes here:

1. The input "read" statement is set up for the test data file test2_5b.dat . This consists of four days of Moana Wave COARE data, 26-29 Nov 1992, prepared from Chris Fairall's hourly data file wavhr2_5.asc dated 31/10/96. A full description of the Moana Wave operations, instruments and data set is given at:

2. Only those observations required by the flux algorithm were extracted from Chris' lines of data, excepting that his independently calculated bulk fluxes are included for comparison.

3. Some parameters are not input, but must be redefined in the code if necessary (e.g., the height of sensors (hum, htm), the bulk temperature sensor depth (ts_depth), needed for calculation of the warm layer effect, and pressure and mixed layer height (pp and zi) if available).

4. Because Chris' Tsea was measured at only 0.05m depth, we have added Ts at 6m depth from Mike Gregg's Advanced Microstructure Profiler (AMP, but called MSP in the file) to demonstrate the warm layer code. The Profiler was operated from the Moana Wave during leg 1, and the data was kindly provided in suitable form for the test file by Hemantha Wijesekera (Oceanography Dept., Oregon State University).

5. The warm layer and/or cool skin code may be bypassed by setting jwarm and/or jcool to zero in the code.

6. To demonstrate the warm layer and cool skin, we output the respective delta-temperatures and the warm layer thickness. Note that dt_warm is the warming across the entire warm layer--only if tk_pwp is less than the sensor depth (ts_depth = 6m in the test case) will T0=ts-dt_cool+dt_warm. Otherwise, a linear profile is assumed, and the appropriate fraction of warming above the bulk sensor calculated. Chris' Tsea at 0.05m depth will generally include most of the warm layer but not the cool skin effect.

7. The Webb correction to latent heat flux and the sensible heat flux due to rainfall are NOT added to these fluxes internally in the code. They are output separately, and may be accounted for at the user's discretion.

Test input file

Date:  YYMMDDHHmmss, YY=year, MM=month, DD=day, HH=hour, mm=minute,ss=sec
U:     true wind speed at 15-m height  m/s
Tsea:  sea surface temp (at about 0.05m depth)  deg.C
Tair:  Vaisala air temperature (about 15 m)  deg.C
qair:  Vaisala air specific humidity (about 15 m)  g/kg
Hsb:   Fairall's bulk sensible heat flux  W/m2
Hlb:   Fairall's bulk latent heat flux   W/m2
Taub:  Fairall's bulk surface stress  N/m2
Rs:    solar irradiance  W/m2
Rl:    downwelling longwave irradiance  W/m2
Rain:  precipitation mm/hr
Lat:   Latitude
Lon:   Longitude
MSP:   AMP temperature at 6m depth  deg.C

Test output file

index:  data line number
xtime:  YYMMDDHHmmss, date and time as read in
hsb:    Fairall's bulk sensible heat flux as read in  W/m2
hlb:    Fairall's bulk latent heat flux as read in   W/m2
taub:   Fairall's bulk surface stress as read in    N/m2
ts:     AMP temperature at 6m depth as read in (rounded)  deg.C
HF:     calculated sensible heat flux   W/m2
EF:     calculated latent heat flux    W/m2
TAU:    calculated surface stress   N/m2
T0:     calculated sea skin temperature   deg.C
Webb:   correction to latent heat flux (to be added)  W/m2
RainF:  sensible heat flux due to precipitation   W/m2
rain:   precipitation mm/hr as read in
dt_cool:  cool skin effect  deg.C
dt_warm:  total warming across warm layer thickness  deg.C
tk_pwp:   warm layer thickness  m


Bradley, E.F., and R.A. Weller, 1995: Third Workshop of the TOGA COARE Air-Sea Interaction (Flux) Working Group. Honolulu, 2-4 Aug 1995. UCAR/TCIPO. UCAR Communications, PO Box 3000, Boulder CO 80307-3000 USA.

Bradley, E.F., and R.A. Weller, 1997: Fourth Workshop of the TOGA COARE Air-Sea Interaction (Flux) Working Group. Woods Hole, 9-11 Oct 1996. UCAR/TCIPO. UCAR Communications, PO Box 3000, Boulder CO 80307-3000 USA.

Bradley, E.F, M.W. Moncrieff and R.A. Weller, 1997: Joint workshop of the TOGA COARE Flux and Oceans Working Groups, and the GEWEX GCSS Working Group 4. Boulder, Colorado, 14-16 May 1997. NCAR/MMM, PO Box 3000, Boulder CO 80307-3000 USA.

Caldwell, D.R. and W.H. Elliott, 1971: Surface stresses produced by rainfall, J. Phys. Oceanog. 1, 145-148.

Fairall, C.W., E.F. Bradley, J.S. Godfrey, G.A. Wick, J.B. Edson, and G.S. Young, 1996a: The cool skin and the warm layer in bulk flux calculations. J. Geophys. Res. 101, 1295-1308.

Fairall, C.W., E.F. Bradley, D.P. Rogers, J.B. Edson, G.S. Young, 1996b: Bulk parameterization of air-sea fluxes for TOGA COARE. J. Geophys. Res. 101, 3747-3764.

Godfrey, J.S., and Beljaars, 1991: J. Geophys. Res. 96, 22043-22048.

Gosnell, R., C.W. Fairall, and P.J. Webster, 1995: The sensible heat flux of rainfall in the tropical ocean. J. Geophys. Res. 100, 18437-18442.

Liu, W.T, K.B. Katsaros and J.A. Businger, 1979: Bulk parameterization of the air-sea exchange of heat and water vapor including the molecular constraints at the interface, J. Atmos. Sci. 36, 1722-1735.

Price, J.F., R.A. Weller and R. Pinkel, 1986: Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing, J. Geophys. Res. 91, 8411-8427.

Saunders, P.M., 1967: The temperature at the ocean-air interface, J. Atmos. Sci. 24, 269-273.

Smith, 1988: J. Geophys. Res. 93, 15467-15472.

Webb, E.K., G.I. Pearman and R. Leuning, 1980: Correction of flux measurements for density effects due to heat and water vapour transfer, Q.J.R. Meteorol. Soc. 106, 85-100.

For more information, please contact:

Chris Fairall
325 Broadway
Boulder, CO 80303 USA
Phone: (303)497-3253
Fax: (303)497-6978


E. Frank Bradley
Centre for Environmental Mechanics
GPO Box 821
Canberra, ACT 2601 AUSTRALIA
Phone: (61) 62 46 5575
Fax: (61) 62 46 5560


David P. Rogers
Scripps Institution of Oceanography
La Jolla, CA 92093-0230 USA
Phone: (619) 534-6412
Fax: (619) 534-7452

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