Air-sea asynchronous coupling scheme (2nd version)
Utilizing previous experience gained within MFSPP and various relevant published
works (see for example Rosati and Miyakoda, 1988; Horton et al., 1997; Castellari et al.,
1998; Korres et al., 2000; Korres et al., 2002; Korres and Lascaratos, 2003) the coupling
between the hydrodynamic (regional/shelf) and the atmospheric models within MFSTEP
is designed in such a way to allow one–way feedback ocean-atmosphere mechanisms to
take place. This means that although the atmospheric model momentum/heat/freshwater
budget is not influenced/corrected by the hydrodynamic model, the latter has some
freedom to adjust the turbulent heat fluxes (evaporative and sensible) and the longwave
radiation flux in accordance with its own surface temperature. This is done through a
well-tuned set of bulk formulae for the computation of momentum, heat and freshwater
fluxes at the air-sea interface using atmospheric data provided by the atmospheric model.
In particular as it is already agreed the atmospheric models will provide 1-hour forecast
fields for a) wind velocity at 10m above sea surface, b) air temperature and relative
humidity (or dew point temperature – see appendix 1) at 2m above sea surface, c) the
cloud cover. The first version of the air-sea coupling scheme assumes that the
atmospheric model provides the net shortwave and the downward longwave radiation
flux terms instead of the cloud cover data. Thus in this version additional bulk formulae
are given for the calculation of the net shortwave and lognwave radiation flux terms.
In what follows we present briefly the theory behind the computation of the heat,
freshwater and momentum fluxes at the sea surface done in the accompanying fortran
code bulk_dis2.f
1. Heat flux boundary condition at the sea surface
The net heat flux at the sea surface is the sum of the radiative, sensible and evaporative
components:
Q  Qr  Qe  Qh (1)
where Q is the net heat flux to the ocean, Qr is the net radiative gain received by the
ocean, Qh is the sensible heat flux and finally Qe is the evaporative heat flux.
1.1 Radiative heat flux
The radiative term Qr in (1) consists of three components: the shortwave radiative gain
received by the ocean Qrs , the net infrared radiation flux emitted by the ocean Qir:
Qr  Qrs  Qir (2)
The calculation of the net shortwave radiative gain at the sea surface Qrs is based on Reed
formula (Reed, 1977) as already done in Rosati and Miyakoda (1988), for the global
ocean and Castellari et al. (1998) for the Mediterranean:
Qrs  Qstot 1  0.62 C  0.0019  1    (3)
In Eq.3 C is the cloud cover (in tenths),  is the solar noon altitude in degrees, Qstot is the
total solar radiation reaching the ocean surface under clear sky and  is the ocean surface
albedo. The ocean surface albedo  is computed as a function of the sun zenith angle for
each grid point from Payne (1972). In cases when Qrs  Qstot (overestimation of Qrs due to
low cloudiness values) Qrs is truncated to Qstot .
The net infrared radiation flux term Qir can be computed according to Bignami formula
(Bignami et al., 1995):
Qir   Ts4   TA4  0.653  0.00535eA   1  0.1762C 2  (4)
or according to May formula (May, 1986):


Qir   TA4 0.4  0.05 eA  4 TA3 Ts  TA  1  0.75C 3.4  (5)


In formulae (4) and (5) ,  are the ocean emissivity and the Stefan-Boltzman constant
respectively, Ts is the sea surface temperature (predicted by the ocean model), TA is the
air temperature at 2 meters above sea surface and eA is the atmospheric vapour pressure
which is proportional to the relative humidity i.e:
eA  r eSAT TA 
(eSAT is the atmospheric saturation vapour pressure, computed through a polynomial
approximation as a function of air temperature, Lowe, 1977).
1.2 Evaporative and sensible heat flux:
The evaporative Qe and sensible Qh heat flux terms are calculated by the ocean model
using the bulk aerodynamic formulae

0.622
(6)
Qe   A LV C E W eSAT TS   r eSAT TA 
pA

Qh   A c p CH W TS  TA  (7)
and the atmospheric data of wind speed W
(at 10-meters above sea surface), air
temperature TA and relative humidity r (at 2-meters above sea surface) as provided by the
atmospheric model at 1-hour intervals. The atmospheric saturation vapour pressure eSAT
in (6) is computed through a polynomial approximation as a function of temperature
(Lowe, 1977). The specific heat capacity of air c p and the atmospheric pressure at sea
level pA are considered as constants.
The sea surface temperature Ts used in (6) and (7) is predicted by the hydrodynamic
model itself, the density of moist air  A is computed by the model as a function of air
temperature and relative humidity and finally the latent heat of vaporization LV is
calculated as a function of sea surface temperature (Gill, 1982).
The turbulent exchange coefficients CE and CH are estimated in terms of air-sea
temperature difference and the wind speed taking into account an atmospheric stability
index (Kondo parameterisation - Kondo, 1975).
2. Freshwater flux/Virtual Salt flux boundary condition at the sea surface
The freshwater flux (FW) or the virtual salt flux (VSF) surface boundary condition
(depending on the model configuration) due to evaporation E and precipitation P are
given by
FW  E  P (8)
VSF   E  P  S (9)
where S is the surface salinity predicted by the ocean model. Precipitation rates are
provided by the atmospheric model at 1-hour intervals while the evaporation rate is
calculated from the evaporative heat flux using
E
Qe
(10)
LV
3. Momentum boundary condition at the sea surface
The calculation of the wind stress fields is based on the transformation of the 1-hour wind
velocity data at 10m above sea surface to x and y components of wind stress following
the formula:
 

   A CD W W
(11)
where A is the density of moist air (computed by the ocean model as a function of air
temperature and relative humidity) , W
is the wind velocity and CD is the drag
coefficient. The drag coefficient is calculated as a function of the wind speed and the airsea temperature difference through the polynomial approximation given by Hellerman
and Rosenstein (1983).
Appendix 1
The relative humidity r (%) can be computed from air temperature and dew point
temperature at 2m above sea surface by forming the ratio of the saturation vapor pressure
over liquid water at dew point temperature and at air temperature:
r
es TDC 
es TAC 
100 (12)
where TDC , TAC are the dew point temperature and the air temperature in degree Celsius
respectively.
The saturation vapor pressure over liquid water es (in mb) at temperature T (expressed in
degree Celsius) is given by Bolton’s formula (Bolton, 1980):
 17.67 T 
es T   6.112 exp 
 (13)
 T  243.5 
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