97
Following non-dimensional analysis, the surface sensible heat flux (SH) and latent
heat flux (LH) can be expressed with formulations similar to Eqs. (14) and (15) as
(18)
(19)
where Cdh and Cdq are empirical drag coefficients for heat and water vapor transport,
respectively, qa is the water vapor mixing ratio at the reference atmospheric level, qs is
the saturation water vapor mixing ratio at the surface, L is the latent heat of evaporation
and {3 is a surface wetness factor (ratio of actual to potential evaporation) which measures
the surface evaporation efficiency and depends on complex soil and vegetation processes
(see section 3). Eqs. (14)-(19) can be considered as a first order turbulence closure for
surface atmospheric fluxes.
Note that qs(Tg) is a highly non-linear function of Tg which, based on thermodynamical
considerations, can be expressed by the formula
.622 es(Tg)
qs = p - .378es (Tg)
(20)
where e. is the saturation vapor pressure
T - 273.16
es(Tg) = 611 exp(a 9
)
Tg - b
(21)
and a and b are constants which differ for water and ice. Accurate fourth and sixth
order polynomial approximations for e s are also available, which are computationally
more efficient than (21) (Brutsaert 1978). Once the drag coefficients, {3 parameter and
surface skin temperatures are known, Eqs. (14)-(19), along with the surface energy budget
equations (7) and (8), allow to close the system of AM equations in terms of variables
explicitly carried by the model. Note that similarly to how the turbulent and net radiative
fluxes are used as lower boundary conditions for AMs, they can be used as upper boundary
conditions for ocean models, thereby providing the coupling interface between ocean and
atmospheric models.
2.2. Basic structure of ESEMs
At this point, we can depict the basic structure of an ESEM seen as interface between
different components of a CSM. iFrom this viewpoint, the essential function of the ESEM
over land is to provide the surface momentum, energy and water fluxes, and the water
and energy budget (including snow pack formation and melting) of a region extending
from a few meters within the soil to the top of a canopy layer, given what we can here
call "lower", "upper" and "lateral" boundary conditions.
Following non-dimensional analysis, the surface sensible heat flux (SH) and latent
heat flux (LH) can be expressed with formulations similar to Eqs. (14) and (15) as
(18)
(19)
where Cdh and Cdq are empirical drag coefficients for heat and water vapor transport,
respectively, qa is the water vapor mixing ratio at the reference atmospheric level, qs is
the saturation water vapor mixing ratio at the surface, L is the latent heat of evaporation
and {3 is a surface wetness factor (ratio of actual to potential evaporation) which measures
the surface evaporation efficiency and depends on complex soil and vegetation processes
(see section 3). Eqs. (14)-(19) can be considered as a first order turbulence closure for
surface atmospheric fluxes.
Note that qs(Tg) is a highly non-linear function of Tg which, based on thermodynamical
considerations, can be expressed by the formula
.622 es(Tg)
qs = p - .378es (Tg)
(20)
where e. is the saturation vapor pressure
T - 273.16
es(Tg) = 611 exp(a 9
)
Tg - b
(21)
and a and b are constants which differ for water and ice. Accurate fourth and sixth
order polynomial approximations for e s are also available, which are computationally
more efficient than (21) (Brutsaert 1978). Once the drag coefficients, {3 parameter and
surface skin temperatures are known, Eqs. (14)-(19), along with the surface energy budget
equations (7) and (8), allow to close the system of AM equations in terms of variables
explicitly carried by the model. Note that similarly to how the turbulent and net radiative
fluxes are used as lower boundary conditions for AMs, they can be used as upper boundary
conditions for ocean models, thereby providing the coupling interface between ocean and
atmospheric models.
2.2. Basic structure of ESEMs
At this point, we can depict the basic structure of an ESEM seen as interface between
different components of a CSM. iFrom this viewpoint, the essential function of the ESEM
over land is to provide the surface momentum, energy and water fluxes, and the water
and energy budget (including snow pack formation and melting) of a region extending
from a few meters within the soil to the top of a canopy layer, given what we can here
call "lower", "upper" and "lateral" boundary conditions.