COARE BULK FLUX ALGORITHM VERSION 2.0 10 August 1994
C.W. Fairall
R/E/ET7
NOAA/ERL
325 Broadway
Boulder, CO 80303 USA
Tel: 303-496-3253
FAX: 303-497-6978
EMAIL: C.Fairall@omnet.com
I. Background
The COARE 2.0 algorithm was developed by C.Fairall, E.F.Bradley,
and D.Rogers. Details are doccumented in papers on the algorithm (Fairall
et al., 1994a) and the cool skin and warm layer effects (Fairall et al.,
1994b). The algorithm is designed to give estimates of the turbulent
fluxes of sensible and latent heat and the stress from inputs of bulk
variables. The bulk transfer coefficients are based on the Liu, Katsaros,
Businger model (JAS, 36, 1722, 1979) with some modifications.
II. COARE version 1.0
Version 1.0 was released in November, 1993. It contained the following
modifications to the basic LKB code:
1. Sea surface humidty, Qs, was expressed as 0.98 times the saturation
humidity of pure water at the sea surface temperature. This was done to
account for the reduction in water vapor pressure by salinity in sea water.
2. The velocity roughness length was specified as the sum of a Charnock
formula and a smooth flow limit as per Smith (JGR, 93, 15467, 1988)
zo = 0.011 u*^2/g + 0.11 nu/u*
where u* is the friction velocity, g the acceration of gravity, and nu the
kinematic viscosity of air.
3. The Monin-Obukhov dimensionless profile functions were given a form
that asymptotically approached the proper convective limit as wind speed
goes to zero. As stability approaches neutral conditions, the function is
blended to a standard Kansas type.
4. The von Karmon constant is set to k=0.4 and dimensionless scalar
gradients have a value of 1.0 at neutral conditions.
5. The LKB specification of temperature and moisture roughness lengths (Rt
and Rq) in terms of velocity roughness Reynolds number, Rr, were retained
but the transfer coefficients for moisture and heat were reducted 15%.
This adjustment was done to give better average agreement with the Moana
Wave flux data from COARE. In the original LKB paper one finds
SQRT(Ctn) = (1/2.2) / ln(z/zot)
This was changed to
SQRT(Ctn) = (1/2.2/1.15) / ln(z/zot)
6. Following Godfey and Beljaars (JGR, 96, 22043, 1991), the wind speed in
the bulk expression is augmented by a gustiness velocity, Wg
u = sqrt[Ux^2 + Uy^2 + Wg^2]
where Ux and Uy are the mean wind components (i.e., magnitude of the mean
wind vector) and Wg is proportional to the convective scaling velocity, W*
Wg = beta W*
A value for beta of 1.2 was chosen based on the Moana Wave data.
III. COARE version 2.0
Version 2.0 was released at the COARE data workshop in Toulouse, France, in
August of 1994. It contained the following changes to the 1.0 version.
1. The specification of Rt and Rq was changed slightly in the Rr range
from 0.13 to 1.0. The basic transfer coefficient expression became
SQRT(Ctn) = k/ln(z/zot)
2. A cool skin model was added to correct bulk water temperatures to true
SST. This model was based on the standard Saunders type (JAS, 24, 269,
1967) with a modification to include the effects of buoyancy flux. This
produces a cool skin of about 0.3 K during the night. During the day the
cool skin may be reduced or eliminated entirely by solar heating in the
upper mm of the ocean.
3. A warm layer model was added to correct bulk water temperature
measurements made at some depth, Zb. The idea is that ship intake and buoy
temperature sensors at a meter or so depth are unable to resolve the
diurnal warm layer common in the COARE region under light wind conditions.
This model was based on a simplified scaling version of the Price Weller
Pinkel mixing model (JGR, 91, 8411, 1986). If daytime solar heating is
sufficient, a stable near-surface layer is formed causing the surface
temperature to increase. Linear profiles of temperature and current are
assumed. The depth is determined by a critical Richardson number (Ri) and
the profile of absorption of solar energy in the water. Ri is set to 0.65
as per PWP. Under very light wind conditions, peak solar warming as great
as 4 K is produced with a warm layer depth of about 0.25 m. Once the warm
layer forms, its depth and intensity are determined by integrating the
accumulated momentum and heat input in the layer. Thus, this model
requires a complete time series of data throughout the diurnal cycle.
Both the cool skin and warm layer can be switched off if true surface
temperature is available (e.g., from aircraft with IR thermometers).
4. The heat flux due to precipitation is estimated as per Gosnell et al.
(1994).
IV. Inputs and Outputs
COARE version 2.0 requires the following inputs:
1. General inputs
Measurement heights for wind speed, air temperature, humidity
Measurement depth for water temperature
Switch setting for cool and warm layers (Jcool, Jwarm)
Longitude or time zone of experiment
Atmospheric inversion height (default 600 m)
Atmopsheric surface pressure (mb)
Reference heights for output means
2. Line inputs
Wind vector magnitude (m/s)
Water temperature (Cel)
Air temperature (Cel)
Humidity: either specific humidity (g/kg) or RH (0 to 1.0)
Downward solar flux (W/m^2)
Downward IR flux (W/m^2)
Precipitation rate (mm/hr)
Note if downward solar is not known, it can be estimated with standard
models if cloud information is available. Also, if downward IR is not
available, it can be estimated as 420 W/m^2 for the COARE area; or, a bulk
model can be used.
The model outputs values for the turbulent fluxes, rain heat flux, warm and
cool layers, plus numerous diagnostic variables such as transfer
coefficients and roughness lengths. Also, the mean data can be
extrapolated to some reference height (e.g, 10-m) specified at the
beginning. This is useful for comparing measurements made at different
heights (e.g., buoy and aircraft).
Fortran (77.f) and Rocky Mountain Basic versions are available. Also, a
set of Fotran programs for driving MATLAB are also available. Additional
programs for the inertial-dissipation flux method and Payne's albedo code
are available.
V. Comments on surface energy budget.
The COARE flux working group recommends the following:
1. Sea surface broadband IR emissivity of 0.97.
2. Average sea surface albedo of 0.055 (otherwise use Payne).
3. Wind speeds should be referenced to the sea surface. In other words,
GPS winds should be corrected for surface currents.
4. Rain is 0.2 K cooler than the droplet wetbulb temperature.
5. The time scale of the average bulk variables used in this algorithm is
on the order of 30 minutes. The use of daily averaged or monthly averaged
variables is not recommended.
6. Measurement heights greater than 50 m should be put
in as 50 m.