Surface Fluxes of Momentum, Heat, and Water Vapor
69
where B is a single empirical constant. This convective form provides a closed form expression
for the sensible heat flux
(3.20)
This method provides a simple and direct computation of sensible heat flux, which does not
require iteration or depend on u •. Below, we will describe how to compute co.
Latent heat flux
Assuming similarity of scalars (see Brutsaert, 1982), we can extend our temperature analysis
to water vapor. In fact, it is reasonable to believe that the result obtained for cI> •• would apply
to any scalar. Therefore, we write the normalized dissipation rate for water vapor as
cqkzu. = B (_-=-)-k
< wq >2
L
B (~r~ [<;; >~] (kzft
(3.21 )
This convective scaling form yields the following expression for evaporation
(3.22)
where < we > is taken in this case from the above calculation based on co. The dissipation
rate for humidity variance can be calculated by the methods described below for temperature
with the substitution of q for e.
Momentum flux
For true convecti ve scaling the dissipation rates of the TKE and scalar variances are independent
of u., and so measurements of the dissipation rates do not contain the information necessary
to estimate u •. For neutral stratification the normalized dissipation rate of TKE is a constant.
This neutral behavior for cI>. seems to continue up to about -z/ L = 0.1 (Albertson et ai.,
1996). In this limited region we may use
and on rearrangement
I
U. = [C-1ckzj'
(3.23)
The momentum flux per unit mass is simply -u~. For larger values of -z/ L we can compute
u. from the empirical interpolation form of cI>. as used by We7l (i.e. (3.Ub)) with H taken
from (3.20) for use in calculating L. Note this requires some iteration. Our main focus here is
in estimating sensible and latent heat (water vapor) fluxes and, therefore, we will not extend
the u. model any further.
In the next section, we review several inertial subrange methods for computing c and co from
velocity and temperature fluctuation measurements.
69
where B is a single empirical constant. This convective form provides a closed form expression
for the sensible heat flux
(3.20)
This method provides a simple and direct computation of sensible heat flux, which does not
require iteration or depend on u •. Below, we will describe how to compute co.
Latent heat flux
Assuming similarity of scalars (see Brutsaert, 1982), we can extend our temperature analysis
to water vapor. In fact, it is reasonable to believe that the result obtained for cI> •• would apply
to any scalar. Therefore, we write the normalized dissipation rate for water vapor as
cqkzu. = B (_-=-)-k
< wq >2
L
B (~r~ [<;; >~] (kzft
(3.21 )
This convective scaling form yields the following expression for evaporation
(3.22)
where < we > is taken in this case from the above calculation based on co. The dissipation
rate for humidity variance can be calculated by the methods described below for temperature
with the substitution of q for e.
Momentum flux
For true convecti ve scaling the dissipation rates of the TKE and scalar variances are independent
of u., and so measurements of the dissipation rates do not contain the information necessary
to estimate u •. For neutral stratification the normalized dissipation rate of TKE is a constant.
This neutral behavior for cI>. seems to continue up to about -z/ L = 0.1 (Albertson et ai.,
1996). In this limited region we may use
and on rearrangement
I
U. = [C-1ckzj'
(3.23)
The momentum flux per unit mass is simply -u~. For larger values of -z/ L we can compute
u. from the empirical interpolation form of cI>. as used by We7l (i.e. (3.Ub)) with H taken
from (3.20) for use in calculating L. Note this requires some iteration. Our main focus here is
in estimating sensible and latent heat (water vapor) fluxes and, therefore, we will not extend
the u. model any further.
In the next section, we review several inertial subrange methods for computing c and co from
velocity and temperature fluctuation measurements.