On the Heat Energy Fluxes in the Non-stationary Surface Boundary Layer
259
Ail terms appearing in Eq. (4) can be computed from our measured physical
quantifies, except the vertical divergence of the turbulent latent heat flux, because,
as mentioned above, the measurement of the latent heat flux at 5 m was not available. The vertical divergence of latent heat flux has then been computed as a residual of the other ones from the conservation Eq. (4). It is possible to
assume [10] that: (1) the molecular conduction of heat kô —is small compared
with the turbulent conduction; and (2) the horizontal divergences of the turbulent
(------- and —---- ) and radiative (—l and —fluxes are small compared
ôx
ôy
dx
’ dy
with the vertical divergences. Finally, assuming a two-dimensional reference System with the wind vector projected into a component relative to the x axis aligned
along the two masts and pointing offshore and its origin fixed at the inner one
and the z axis upward, Eq. (4) becomes:
dddH
dQ
dd
dF
pcD----- =-------- +-------- pc„u-------------- .
p dt
dz
dz
p dx
dz
(5)
The local term (pcn----- ), the horizontal advection term (pcnu ----- ) and the
pdt
pdx
vertical divergence terms
, ^-) of turbulent fluxes [H and F, as defined in
dz
dz
eqs. (2) and (3)] are approximated by the finite différences of the mean quantifies
measured (or computed) by the slow and fast response instruments, while the net
radiative flux (Q) is computed by the équation:
Q = Rs(l-as) + Rld-Rlu>
(6)
where Rs is the (global) short-wave radiation (from 0.3 to 1.1 pm), as is the albedo of the surface, Rld is the downward long-wave atmospheric radiation and R)u is
the upward long-wave radiation from iced surface.
The global short-wave radiation Rs is measured by the Sitep solarimeter, while
the other physical quantifies in Eq. (6) are parametrized by some spécifie relationships [11-14] that, making use of the température and the humidity measured
at 10 and 5 m by the other Sitep sensors, allow us to estimate the vertical divergence of the net radiative flux Q. These relationships are: Rlu = esoTs4 +(I—Es)Rld
[11] and Rld = eacoTa4 [12], where £s is the emissivity at the surface, o is the constant of Bolzmann, Tsp is the skin température of ice surface, Ta is the air température and eac is the atmospheric emissivity [£fl<. = 0.67(ea)°08 [13], with
ea = rh • 6.112exp[17.67(Tfl-273.15) / (Tfl-29.65)] [14], where ea is the atmospheric vapour pressure and rh is the relative humidity].
The empirical équations we hâve used to estimate the vertical divergence of the
radiative flux show two limitations; the first one is that they do not take the cloudiness into account; the second one is that they use the atmospheric humidity measured at about 5 km apart. Even if this is not important to the aim of the présent
work, because the vertical divergence of this flux is very small and the sky was
259
Ail terms appearing in Eq. (4) can be computed from our measured physical
quantifies, except the vertical divergence of the turbulent latent heat flux, because,
as mentioned above, the measurement of the latent heat flux at 5 m was not available. The vertical divergence of latent heat flux has then been computed as a residual of the other ones from the conservation Eq. (4). It is possible to
assume [10] that: (1) the molecular conduction of heat kô —is small compared
with the turbulent conduction; and (2) the horizontal divergences of the turbulent
(------- and —---- ) and radiative (—l and —fluxes are small compared
ôx
ôy
dx
’ dy
with the vertical divergences. Finally, assuming a two-dimensional reference System with the wind vector projected into a component relative to the x axis aligned
along the two masts and pointing offshore and its origin fixed at the inner one
and the z axis upward, Eq. (4) becomes:
dddH
dQ
dd
dF
pcD----- =-------- +-------- pc„u-------------- .
p dt
dz
dz
p dx
dz
(5)
The local term (pcn----- ), the horizontal advection term (pcnu ----- ) and the
pdt
pdx
vertical divergence terms
, ^-) of turbulent fluxes [H and F, as defined in
dz
dz
eqs. (2) and (3)] are approximated by the finite différences of the mean quantifies
measured (or computed) by the slow and fast response instruments, while the net
radiative flux (Q) is computed by the équation:
Q = Rs(l-as) + Rld-Rlu>
(6)
where Rs is the (global) short-wave radiation (from 0.3 to 1.1 pm), as is the albedo of the surface, Rld is the downward long-wave atmospheric radiation and R)u is
the upward long-wave radiation from iced surface.
The global short-wave radiation Rs is measured by the Sitep solarimeter, while
the other physical quantifies in Eq. (6) are parametrized by some spécifie relationships [11-14] that, making use of the température and the humidity measured
at 10 and 5 m by the other Sitep sensors, allow us to estimate the vertical divergence of the net radiative flux Q. These relationships are: Rlu = esoTs4 +(I—Es)Rld
[11] and Rld = eacoTa4 [12], where £s is the emissivity at the surface, o is the constant of Bolzmann, Tsp is the skin température of ice surface, Ta is the air température and eac is the atmospheric emissivity [£fl<. = 0.67(ea)°08 [13], with
ea = rh • 6.112exp[17.67(Tfl-273.15) / (Tfl-29.65)] [14], where ea is the atmospheric vapour pressure and rh is the relative humidity].
The empirical équations we hâve used to estimate the vertical divergence of the
radiative flux show two limitations; the first one is that they do not take the cloudiness into account; the second one is that they use the atmospheric humidity measured at about 5 km apart. Even if this is not important to the aim of the présent
work, because the vertical divergence of this flux is very small and the sky was