The turbulent diffusion coefficient is evaluated by the formula of
Klemp and Wilhelmson (1978), where
the turbulent diffusion is proportional to square root of turbulent
kinetic energy .
The value of turbulent diffusion coefficient for heat is equal
to that for momentum.
The diagnostic equation of turbulent kinetic energy is as follows.

.
and are generation terms of the turbulent kinetic
energy associated with buoyancy force and wind shear, respectively.

where is the mixing length which is the smaller value of either vertical grid interval or altitude.

The last term in left hand side of (10)
represents the dissipation rate of turbulent kinetic energy.
By using this term, in equation (5)
is given as follows.

The surface momentum and heat fluxes are given by the bulk
formulae, where the bulk coefficients depend on static stability
and vertical wind shear (Louis, 1979).
The bulk coefficient for heat transport has same value of that for
momentum.

are the horizontal wind and temperature at the lowest level of the model atmosphere . is the surface temperature. The bulk coefficient is calculated as follows.

where,

(18) |

and is the Karman constant (= 0.35), is the roughness length. is the bulk Richardson number, which is given as follow.

where and are the potential temperature and that of horizontal mean value at the lowest level of model atmosphere.

Parameters | Standard values | Note |

0.35 | ||

1 cm | Sutton et al., (1978) |